MODELOS PARA PRECIFICAÇÃO DE OPÇÕES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

Embed Size (px)

Citation preview

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    1/118

    MLTTE,UI_G

    KLJEAL] T@_@ T_EMCICM@M @L JE LTM LE]7 UK@ @OL_J@BEK

    O@SE]C@H@ T@_@ E]ZCK@_ @ YLA@ZCACJ@JE

    Ychcmcu} Orczl _lmn`

    Jc}}erz`ml je Ke}zr`jl `tre}ehz`j` `l

    Trlbr`k` je Tl}+br`ju`ml ek Ehbehn`rc`

    je Trljuml! MLTTE! j` Uhcyer}cj`je

    Iejer`a jl _cl je G`hecrl! mlkl t`rze jl}

    repuc}czl} heme}}rcl} d lozehml jl zzual je

    Ke}zre ek Ehbehn`rc` je Trljuml(

    Lrcehz`jlr7 Neacl jl} ]`hzl} Kcblh

    _cl je G`hecrl

    K`rml je ?443

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    2/118

    KLJEAL] T@_@ T_EMCICM@M @L JE LTM LE]7 UK@ @OL_J@BEK

    O@SE]C@H@ T@_@ E]ZCK@_ @ YLA@ZCACJ@JE

    Ychcmcu} Orczl _lmn`

    JC]]E_Z@M @L ]UOKEZCJ@ @L ML_TL JLMEHZE JL CH]ZCZUZL

    @AOE_ZL AUCW MLCKO_@ JE T L]+B_@JU@M @L E TE]PUC]@ JE

    EHBEHN@_C@ .MLTTE# J@ UHCYE_]CJ@JE IEJE_@A JL _CL JE

    G@HEC_L MLKL T@_ZE JL] _EPUC]CZL] HEME]]@_CL] T@_@ @

    LOZEHM @L JL B_@U JE KE]Z_E EK MCEHMC@] EK EHBEHN@_C@ JE

    T_LJUM @L(

    @trly`j` tlr7

    Trli( Neacl jl} ]`hzl} Kcblh ! Tn(J(

    Trli( Ycrbacl Gl}e K`rzch} Ierrecr` Icanl! J(]m(

    Trli( Mrc}zc`hl @ubu}zl Mleanl Ierh`hje}! Tn(J(

    _CL JE G@HEC_L! _G O_@]CA

    K@_M L JE ?443

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    3/118

    _lmn`! Ychcmcu} Orczl

    Kljeal} t`r` Tremcffm`ml je Ltmle}7 Uk` @olrj`bek

    O`se}c`h` t`r` E}zck`r ` Yla`zcacj`je,Ychcmcu} Orczl

    _lmn`( _cl je G`hecrl7 UI_G,MLTTE! ?443(

    ^YCCC! 044 t(7 ca(6 ?3! 2mk(

    Lrcehz`jlr7 Neacl jl} ]`hzl} Kcblh

    Jc}}erz`ml .ke}zr`jl# UI_G,MLTTE,Trlbr`k` je

    Ehbehn`rc` je Trljuml! ?443(

    _eierehmc`} Ocoaclbrffm`}7 t( 32 33(

    0( Tremcffm`ml je Ltmle}( ?( Chierehmc O`se}c`h`(

    =( ]ckua`ml E}zlm}zcm`( C( ! Neacl jl} ]`hzl} Kcblh(

    CC( Uhcyer}cj`je Iejer`a jl _cl je G`hecrl! MLTTE!

    Trlbr`k` je Ehbehn`rc` je Trljuml( CCC( Zzual(

    ccc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    4/118

    @ kchn` k`e! Yer` Aumc` Orczl

    jl} ]`hzl}! pue ke jec~lu

    ehpu`hzl mlhmauc` e}z`

    jc}}erz`m`l( Ea` jejcmlu }u` ycj`

    d kck( ]`uj`je} ezerh`}

    .ch keklrc`k#(

    cy

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    5/118

    @br`jemckehzl}

    @ kuaner j` kchn` ycj`! @ae}}`hjr`! }ek ea` ` mlhmau}l je}z` jc}}erz ml hl }erc`

    tl}}yea( ` kchn` i`kac`! ek e}temc`a Ierh`hjl Tckehz`! Hca` K`rc` e Ieacte M`r+

    jl}l( @ kchn` }lbr` K`rc` @acme( `l} keu} `kcbl} Bu}z`yl Re}zch! Ych`s Mn`o`!

    T`zrmc` K`rpue}! e `l} crkl} @rznur Hezl e @ae~`hjre K`rpue}( @ Bucanerke

    Or`cae! tea` mla`olr`ml }lore l kerm`jl ffh`hmecrl je ltmle}( @ zurk` je 0339

    jl Mlaebcl Hlzre J`ke! @heac}e ]`mf}! Mrc}zc`he M`}}`r! Mrc}zc`he _`oeal! Bu}z`yl

    Fhu}z! Guac`h` M`rhecrl! Aelh`rjl Lacyecr`! Aumc`h` Ml}z`! Aumc`h` K`c`! K`rcl

    Bucanerke! H`z`ace K`rzch}! T`ua` M`rjl}l! ]`ual K`rpue}! T`ua` K`aui! `l} je+

    k`c} pue hl ilr`k kehmclh`jl} e `l trlie}}lr Glrbe Mlrre`( @} `kcb`} j` kchn`

    ke! pue ke `tlc`r`k `tl} }u` t`rzcj`! ek e}temc`a `} crk} ]cayhc` e K`r}ean`

    B`rmc`! e ` K`rc Mrc}zch` ]`rkehzl( @l Mlh}eanl H`mclh`a je Je}ehylayckehzl

    Mcehzffml e Zemhlalbcml + MHTp teal `tlcl ffh`hmecrl( @l} trlie}}lr Neacl ]`hzl}

    Kcblh! tlr }u` lrcehz`ml! e M`ral} @o`hzl Y`aae! tlr }u` mla`olr`ml chzeh}cy`(

    @l} Trlie}}lre} jl TET ]`kuea Gurfcecmw! Ycrbacl Gl}e K`rzch} Ierrecr` Icanl(

    @l trlie}}lr Mrc}zc`hl @ubu}zl Mleanl Ierh`hje}! te}puc}`jlr jl Jet`rz`kehzl

    je Ehbehn`rc Eaezrcm` j` TUM( @ }emrezrc` j` re` je te}puc}` lter`mclh`a jl

    TET! @hjrec` Ack`( @ MLHZ@^! teal `tlcl d mlhmau}l je}ze zr`o`anl! ek e}te+

    mc`a d Berehmc` je Ta`heg`kehzl E}zr`zebcml je Zriebl ek e}temc`a d @ae}}`hjrl

    Kecr`! K`smlh j` Turew` ^`ycer! Gll Chmcl ]`ab`jl Gr e _`i`ea Lacyecr`(

    y

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    6/118

    _e}ukl j` Jc}}erz`ml `tre}ehz`j` d MLTTE,UI_G mlkl t`rze jl} repuc}czl}

    heme}}rcl} t`r` ` lozehml jl br`u je Ke}zre ek Mcehmc`} .K(]m(#

    KLJEAL] T@_@ T_EMCICM@M @L JE LTM LE]7 UK@ @OL_J@BEK

    O@SE]C@H@ T@_@ E]ZCK@_ @ YLA@ZCACJ@JE

    Ychcmcu} Orczl _lmn`

    K`rml,?443

    Lrcehz`jlr7 Neacl jl} ]`hzl} Kcblh

    Trlbr`k`7 Ehbehn`rc` je Trljuml

    Hl mlhze~zl jl kerm`jl ffh`hmecrl je `mle} e ltmle}! e}z` jc}}erz`ml trltle uzc+

    acw`r ` chilrk`ml mlhzcj` ek treml} nc}zlrcml} je ltmle}! t`r` e}zck`r ` yla`zcacj`je

    je uk `zcyl! e ehzl tremcffm`r hly`} ltmle}( @ t`rzcr jl} kljeal} je zektl mlhzhul

    ilr`k uzcacw`j`} ju`} `olrj`beh}( Uk` lhje l trloaek` e `olrj`jl }utlhjl `

    yla`zcacj`je jl `zcyl chy`rc`hze `l alhbl jl zektl! ` t`rzcr jl kljeal Oa`mf `hj

    ]mnlae} + .O]# e luzr` ` t`rzcr je uk` e}zruzur` je yla`zcacj`je e}zlm}zcm`! uzc+

    acw`hjl l kljeal Nuaa `hj Rncze + .NR#( L trloaek` je e}zck`ml j` yla zcacj`je

    e zr`z`jl tea` lzcm` j` e}z`z}zcm` o`se}c`h` e je kezljl} mlktuz`mclh`akehze ch+

    zeh}cyl}( E}z` jc}}erz`ml uzcacw` j`jl} }ckua`jl} t`r` `y`ac`r l} `ablrczkl} e `l

    ffh`a re`acw` uk e~terckehzl mlk j`jl} re`c} jl kerm`jl ffh`hmecrl(

    yc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    7/118

    @o}zr`mz li Jc}}erz`zclh tre}ehzej zl MLTTE,UI_G `} ` t`rzc`a iuaffaakehz li zne

    repucrekehz} ilr zne jebree li K`}zer li ]mcehme .K(]m(#

    KLJEA] ZL T_CME LTZCLH]7 @ O@SE]C@H @TT_L@MN ZL E]ZCK@ZE

    ZNE YLA@ZCACZS

    Ychcmcu} Orczl _lmn`

    K`rmn,?443

    @jyc}lr7 Neacl jl} ]`hzl} Kcblh

    Jet`rzkehz7 Trljumzclh Ehbcheerchb

    Ch zne mlhze~z li zne ffh`hmc`a k`rfez li }n`re} `hj ltzclh}! znc} zne}c} trltl}e}

    zl u}e chilrk`zclh irlk nc}zlrcm`a trcme} li ltzclh}! zl e}zck`ze zne yla`zcaczs `h

    `}}ez! `hj zneh tremcffm r ` he ltzclh( Irlk zne mlhzchulu}+zcke kljea} ere u}ej

    zl `ttrl`mne}( Lhe nere zne c}}ue c} `jjre}}ej ci zne yla`zcaczs li `}}ez chy`rc`hz

    lyer zcke! u}chb zne Oa`mf `hj ]mnlae} kljea + .O]# `hj `hlzner irlk ` }zrumzure

    li }zlmn`}zcm yla`zcaczs! u}chb zne kljea Nuaa `hj Rncze + .NR#( Zne trloaek li

    e}zck`zchb yla`zcaczs c} zre`zej os zne ter}temzcye li O`se}c`h }z`zc}zcm`a keznlj}

    `hj mlktuz`zclh`aas chzeh}cye( Znc} jc}}erz`zclh u}e} }ckua`zej j`z` zl ey`au`ze zne

    `ablrcznk} `hj terilrk ` ffh`a e~terckehz czn re`a j`z` li zne ffh`hmc`a k`rfez(

    ycc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    8/118

    ]ukrcl

    Ac}z` je Icbur`} ~

    Ac}z` je Z`oea`} ~y

    Ac}z` je ]kolal} ~yc

    0 Chzrljuml 0

    ? Trlme}}l je Zektl Mlhzhul =

    ?(0 Trlme}}l je Czl ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( :

    ?(? Ltmle} e l Kljeal je Oa`mf `hj ]mnlae} + O] ( ( ( ( ( ( ( ( ( ( ( ( ( 5

    ?(?(0 @ Nctlze}e je Kuhjl _c}ml+Heuzrl ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >

    ?(= L Kljeal je Nuaa Rncze + NR ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 04

    = Chierehmc` e Mlktuz`ml O`se}c`h` 0:

    =(0 Zelrek` je O`se} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 0:

    =(? Klhze M`ral Yc` M`jec` je K`rfly ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 09

    =(= Kezrltlac} N`}zchb} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 09

    =(: @kl}zr`jlr je Bcoo} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 02

    =(5 Kljeal} Jchkcml} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 0>

    =(5(0 Kljeal Ache`r Jchkcml Hlrk`a ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ?4

    : Kljeal} mlk Yla`zcacj`je Chy`rc`hze hl Zektl ?=

    :(0 Yla`zcacj`je Chy rc`hze mlk Chilrk`ml jl _ezlrhl + Kljeal ` ( ( ( ( ?=

    :(? Yla`zcacj`je Chy rc`hze mlk Chilrk`ml jl} _ezlrhl} e je Ltmle} ( ( ?3

    :(?(0 Yla`zcacj`je Chy rc`hze mlk Chilrk`ml jl _ezlrhl e je Uk`

    Ltml + Kljeal o ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ?3

    yccc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    9/118

    :(?(? Yla`zcacj`je Chy`rc`hze mlk Chilrk`ml jl _ezlrhl e je Ju`}

    Ltmle} + Kljeal m ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( =9

    :(= Yla`zcacj`je Cktamcz` ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( :0

    5 Kljeal} mlk Yla`zcacj`je E}zlm}zcm` :=

    5(0 Yla`zcacj`je E}zlm}zcm` mlk Chilrk`ml jl _ezlrhl + Kljeal j ( ( ( :=

    5(0(0 @ablrczkl Il`rj Icazerchb O`mf`rj ]`ktachb + IIO] ( ( ( :9

    5(0(? ]ckua`ml ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( :3

    5(? Yla`zcacj`je E}zlm}zcm` mlk Chilrk`ml jl _ezlrhl e Ltml + Klj+

    eal e ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 94

    9 E~terckehzl mlk J`jl} jl Kerm`jl Ich`hmecrl H`mclh`a 24

    9(0 @} Ltmle} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 20

    9(? Kljeal ` mlkl J`jl} jl @zcyl TEZ_: ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 2:

    9(= Kljeal o mlk J`jl} jl @zcyl TEZ_: e jl Nc}zlrcml je Ltmle}

    Uhcffm`j`} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 22

    9(: Kljeal j mlk J`jl} jl @zcyl TEZ_: ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >?

    9(5 Kljeal e mlk J`jl} jl @zcyl TEZ_: e jl Nc}zlrcml je Ltmle}

    Uhcffm`j`} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >9

    9(9 _e}uaz`jl} ]uk`rcw`jl} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 30

    2 Mlhmau}l 35

    _eierehmc`} Ocoaclbrffm`} 32

    c~

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    10/118

    Ac}z` je Icbur`}

    :(0 Treml} ]Z ; .}z!(((!}Z# }ckua`jl} uzcacw`hjl ` epu`ml ?(0= e l}

    t`rkezrl}7 ; 4(9> e ? ; 4(??( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ?5

    :(? _ezlrhl} SZ ; .sz!(((!sZ# t`r l `zcyl }ckua`jl( ( ( ( ( ( ( ( ( ( ( ( ( ?5

    :(= Nc}zlbr k`} e m`jec` t`r` `kl}zr` j` jc}zrcoucmle} ` tl}zerclrc je

    e ? + kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ?9

    :(: @zcyl }ckua`jl t`r` `kl}zr` ze}ze! treyc}l e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ?2

    :(5 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl }ckua`jl t`r` ` `kl}zr`

    ze}ze + kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ?>:(9 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl treyc}zl + kljeal `( ( ( ( ?>

    :(2 Ltml ber`j` t`r` `kl}zr` ze}ze LZ ; .l0!(((!lZ#! mlk Z;0=4( ( ( ( =?

    :(> Nc}zlbr`k`} e m`jec` t`r` `kl}zr` j` jc}zrcoucmle} ` tl}zerclrc je !

    ? e ?+ kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ==

    :(3 @zcyl }ckua`jl t`r` `kl}zr` ze}ze! treyc}l e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( =::(04 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl }ckua`jl t`r` ` `kl}zr`

    ze}ze + kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( =5

    :(00 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl treyc}zl hl t`}}l 5 +

    kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( =5

    :(0? Treml} }ckua`jl} j`} ltmle} L0Z e L?Z ` t`rzcr jl kljeal m( ( ( ( ( ( =>

    ~

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    11/118

    :(0= Nc}zlbr k`} e m`jec`} t`r` `kl}zr` j` jc}zrcoucmle} ` tl}zerclrc je

    ! ?0 !?0

    e ? + kljeal m( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( :4

    :(0: Y`alre} lozcjl} t`r` ` yla zcacj`je} uzcacw`hjl l `ablrczkl ltzckcwe ( :?

    :(05 Y`alre} lozcjl} t`r` ` yla zcacj`je} uzcacw`hjl l `ablrczkl hak ( ( ( ( :?

    5(0 Y`alre} }ckua`jl} t`r` `kl}zr zrechl jl `zcyl ]z! je `mlrjl mlk l

    kljeal j! e t`rkezrl} ; 4(4405 ; 4(?5! ; 4(32 e ? ; 4(49?5( 545(? Jc`br`k` t`r` l kljeal j ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 50

    5(= Nc}zlbr`k` e M`jec` t`r `kl}zr` j` jc}zrcoucml ` tl}zerclrc jl}

    t`rkezrl} ! e ? + kljeal j }chbae klye( ( ( ( ( ( ( ( ( ( ( ( ( ( 5=

    5(: Yla`zcacj`je E}zlm}zcm` }ckua`j`! y`alre} e}zck`jl} e chzery`al} mlk

    35% je mrejcocacj`je + kljeal j }chbae klye( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 5:

    5(5 @zcyl `kl}zr` ze}ze! treyc}l e chzery`al} mlk 35% je mrejcocacj`je

    j` jc}zrcoucml trejczcy` t.}Z&0!(((!}Z&=4# + kljeal j }chbae klye( ( ( 5:

    5(9 Ltml }ckua`j` t`r `kl}zr` ze}ze! treyc}l e chzery al} mlk

    35% je mrejcocacj`je! lozcjl} ` t`rzcr j` jc}zrcoucml `kl}zr a

    t.NR.}Z&0! yZ&0! j ; =4#!(((!NR.}Z&=4! yZ&=4! j ; 4##! mlk l `zcyl

    j` `kl}zr` ze}ze + kljeal j }chbae klye( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 55

    5(2 Ltml }ckua`j` t`r `kl}zr` ze}ze! treyc}l e chzery al} mlk

    35% je mrejcocacj`je! lozcjl} ` t`rzcr j` jc}zrcoucml `kl}zr a

    t.NR.}Z&0! yZ&0! j ; =4#!(((!NR.}Z&=4! yZ&=4! j ; 4##! mlk `zcyl

    treyc}zl teal `ablrczkl + kljeal j }chbae klye( ( ( ( ( ( ( ( ( ( ( ( ( 59

    5(> Nc}zlbr`k` e M`jec` t`r `kl}zr` j` jc}zrcoucml ` tl}zerclrc jl}

    t`rkezrl} ! e ? + kljeal j IIO]( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 52

    5(3 Yla`zcacj`je e}zlm}zcm` }ckua`j`! y`alre} e}zck`jl} e chzery`al} mlk

    35% je mrejcocacj`je + kljeal j IIO]( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 5>

    5(04 @zcyl }ckua`jl mlkl `kl}zr` ze}ze! y`alre} treyc}zl} e chzery`+

    al} mlk 35% je mrejcocacj`je j` jc}zrcoucml `kl}zr a trejczcy`

    t.}Z&0!(((!}Z&=4# + kljeal j IIO]( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 53

    5(00 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml NR e chzery`al} mlk

    35% je mrejcocacj`je( _e}uaz`jl} lozcjl} ` t`rzcr j` jc}zrcoucml

    `kl}zr`a t.NR.}Z&0! yZ&0! j ; =4#!(((!NR.}Z&=4! yZ&=4! j ; 4##!mlk `zcyl }ckua`jl t`r` `kl}zr` ze}ze + kljeal j IIO]( ( ( ( ( ( ( ( 53

    ~c

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    12/118

    5(0? Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml NR e chzery`al} mlk

    35% je mrejcocacj`je( _e}uaz`jl} lozcjl} ` t`rzcr j` jc}zrcoucml

    `kl}zr`a t.NR.}Z&0! yZ&0! j ; =4#!(((!NR.}Z&=4! yZ&=4! j ; 4##!

    mlk l `zcyl treyc}zl + kljeal j IIO]( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 945(0= Jc`br`k` t`r` l kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 9:

    5(0: Nc}zlbr`k` e M`jec` j` `kl}zr` j` jc}zrcoucml ` tl}zerclrc jl}

    t`rkezrl} ! ! ? e ? + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 99

    5(05 Yla`zcacj`je e}zlm}zcm` }ckua`j`! e}zck`y`} e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 99

    5(09 @zcyl }ckua`jl mlkl `kl}zr` ze}ze e re}uaz`jl} j` jc}zrcoucml trej+

    czcy` t.}Z&0!(((!}Z&=4# + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 92

    5(02 Ltml }ckua`j` mlkl `kl}zr ze}ze e re}uaz`jl} j` jc}zrcoucml

    `kl}zr`a t.NR.}Z&0! yZ&0! j ; =4#!(((!NR.}Z&=4! yZ&=4! j ; 4##

    mlk l `zcyl }ckua`jl! tremcffm`ml lozcj` e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 9>

    5(0> Ltml }ckua`j` mlkl `kl}zr` ze}ze e _e}uaz`jl} j` jc}zrcoucml

    `kl}zr`a t.NR.}Z&0! yZ&0! j ; =4#!(((!NR.}Z&=4! yZ&=4! j ; 4## u}+

    `hjl l `zcyl treyc}zl! tremcffm`ml lozcj` e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 9>

    5(03 _e}uaz`jl} t`r` Yla zcacj`je e}zlm}zcm` jl kljeal j e e + kljeal e( 93

    9(0 Treml} t`r l `zcyl Tezrlor } + TH( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 24

    9(? _ezlrhl} t`r` l `zcyl Tezrlor`} + TH( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 20

    9(= Ltmle} TEZ_@34! TEZ_O34! TEZ_M34! TEZ_J34! TEZ_E34 e

    TEZ_I34! `tre}ehz`j`} je ilrk` re}temzcy `l alhbl jl zektl( ( ( ( 2?

    9(: Nc}zlrcml je treml} uhcffm`jl t`r` TEZ_@34! TEZ_O34! TEZ_M34!

    TEZ_J34! TEZ_E34 e TEZ_I34( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 2=

    9(5 Nc}zlbr k`} e m`jec`} t`r` `kl}zr j` jc}zrcoucml ` tl}zerclrc je

    e ? e}zck`j } ` t rzcr jl `zcyl TEZ_:( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 25

    9(9 @zcyl TEZ_:! treyc}le}! chzery`al} mlk 35% je mrejcocacj`je e

    `kl}zr` ze}ze! re}uaz`jl} j` jc}zrcoucml trejczcy` t.}0?4!(((!}05?#! u}+

    `hjl l kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 25

    ~cc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    13/118

    9(2 Treml} j` jc}zrcoucml t.O].}0?4! jc! Fc ; 34#!(((!O].}05?! jc! Fc ;

    34##! lozcjl} ` t`rzcr j` `kl}zr` ze}ze .}0?4!(((!}05?# jl `zcyl u}`hjl

    l kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 29

    9(> Treml} j` jc}zrcoucml t.O].}

    0?4! jc! Fc ; 34#!(((!O].}

    05?! jc! Fc ;34##! lozcjl} ` t`rzcr jl} y`alre} treyc}zl} == t`}}l} ` irehze

    .}0?4!(((!}05?# u}`hjl l kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 29

    9(3 Nc}zlbr`k`} e m`jec } t`r `kl}zr` j` jc}zrcoucml ` tl}zerclrc je !

    ? e ? e}zck`j`} ` t`rzcr jl `zcyl TEZ_: e jl nc}zlrcml uhcffm`jl

    j`} ltmle} TEZ_@34! TEZ_O34! TEZ_M34! TEZ_J34! TEZ_E34

    e TEZ_I34( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 2>

    9(04 Nc}zlbr k` j` jc}zrcoucml ` tl}zerclrc ? jl} kljeal} ` e kljeal o( 23

    9(00 @kl}zr` ze}ze jl `zcyl TEZ_:! treyc}le}! chzery`al} mlk 35% je

    mrejcocacj`je lozcjl} j` jc}zrcoucml trejczcy` t.}0?4!(((!}05?#! u}`hjl

    l kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 23

    9(0? @kl}zr` ze}ze t`r` l} treml} j` ltmle} uhcffm`jl! re}uaz`jl} j` jc}+

    zrcoucml t.O].]0?4! jc! Fc ; 34#!(((!O].]05?! jc! Fc ; 34## mlk `

    `kl}zr` ze}ze je TEZ_:! u}`hjl l kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( 23

    9(0= @kl}zr` ze}ze jl nc}zlrcml uhcffm`jl je ltmle} e re}uaz`jl} j` jc}+

    zrcoucml t.O].}0?4! jc! Fc ; 34#!(((!O].}05?! jc! Fc ; 34## mlk `

    `kl}zr` ze}ze je TEZ_:! u}`hjl l kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( >4

    9(0: Tremcffm`mle} uzcacw`hjl ` jc}zrcoucml oa` oa` oa` t.O].]0?4! jc! Fc ;

    34#!(((!O].]05?! jc! Fc ; 34##! t`r` l kljeal ` e l kljeal o( ( ( ( ( ( >0

    9(05 Nc}zlbr k`} e m`jec`} t`r` ` `kl}zr` j` jc}zrcoucml ` tl}zerclrc je

    ! e ? + kljeal j( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >=

    9(09 Yla`zcacj`je e}zlm}zcm` e}zck`j` e chzery`al} mlk 35% je mrejcocac+

    j`je ` t`rzcr j` `kl}zr` zrechl jl `zcyl TEZ_:! u}`hjl l kljeal

    j( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >:

    9(02 @kl}zr` ze}ze jl `zcyl TEZ_: e re}uaz`jl} lozcjl} mlk ` jc}+

    zrcoucml trejczcy` t.}0?4!(((!}05?# + kljeal j ( ( ( ( ( ( ( ( ( ( ( ( ( ( >:

    9(0> @kl}zr` ze}ze jl nc}zlrcml uhcffm`jl j`} ltmle} e re}uaz`jl} j` jc}+

    zrcoucml t.NR.}0?4! jc! Fc ; 34#!(((!NR.}05?! jc! Fc ; 34##! tremc+

    ffm`mle} e chzery`al} mlk 35% je mrejcocacj`je + kljeal j( ( ( ( ( ( ( ( >5

    ~ccc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    14/118

    9(03 @kl}zr` ze}ze jl nc}zlrcml uhcffm`jl j`} ltmle} e re}uaz`jl} j` jc}+

    zrcoucml t.NR.}0?4! jc! Fc ; 34#!(((!NR.}05?! jc! Fc ; 34##! tremc+

    ffm`mle} e chzery`al} mlk 35% je mrejcocacj`je + kljeal j( ( ( ( ( ( ( ( >5

    9(?4 M`jec`} e nc}zlbr k`} t`r` ` `kl}zr` j` jc}zrcoucml ` tl}zerclrc je! ! ? e

    ?! t`r` TEZ_: nc}zlrcml je ltmle} + kljeal e( ( ( ( ( ( ( >2

    9(?0 Yla`zcacj`je E}zlm}zcm`! chzery`al} mlk 35% je mrejcocacj`je! u}`hjl

    ` `kl}zr` zrechl jl `zcyl TEZ_: e jl nc}zlrcml je ltmle} uhcim`j`}

    + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >>

    9(?? @kl}zr` ze}ze je TEZ_: e re}uaz`jl} j` jc}zrcoucml trejczcy` je

    t.}0?4!(((!}05?# jl kljeal j e jl kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >3

    9(?= @kl}zr` ze}ze jl nc}zlrcml uhcffm`jl} je treml} j`} ltmle} e re}uaz`+

    jl} j` jc}zrcoucml t.NR.}0?4! jc! c#!(((!NR.}05?! jc! c## mlk u}l j`

    `kl}zr` ze}ze je TEZ_: + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >3

    9(?: @kl}zr` ze}ze jl nc}zlrcml uhcffm`jl} je treml} j`} ltmle} e re}ua+

    z`jl} j` jc}zrcoucml t.NR.}0?4! jc! c#!(((!NR.}05?! jc! c## m`amua`jl

    mlk y`alre} treyc}zl} .}0?4!(((!}05?# t`r` TEZ_: + kljeal e( ( ( ( ( ( 34

    ~cy

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    15/118

    Ac}z` je Z`oea`}

    :(0 _e}ukl j`} Jc}zrcoucmle} Tl}zerclrc} je e ? + kljeal ` ( ( ( ( ( ( ?2

    :(? _e}ukl j`} Jc}rcoucmle} jl} t`rkezrl} ! ? e ? + kljeal o( ( ( ( ==

    :(= _e}ukl j`} Jc}zrcoucmle} Tl}zerclrc} je ! ?

    0! ?

    0e ? + kljeal m ( :0

    5(0 Kc}zur` 2+Hlrk`c} ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( :2

    5(? _e}uaz`jl re}ukcjl j`} jc}zrcoucmle} ` tl}zerclrc jl} t`rkezrl} !

    e ? + kljeal j }chbae klye( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 5=

    5(= _e}ukl j` jc}zrcoucml tl}zerclrc t`r` l} t`rkezrl} ! e ? +

    kljeal j IIO]( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 52

    5(: Je}ycl t`jrl jl} t`rkezrl} ! e ?! t`r` l kljeal j mlk `abl+

    rczkl + ]chbae Klye e `ablrczkl + IIO]( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 5>

    5(5 _e}ukl jl} re}uaz`jl} j`} jc}zrcoucmle} ` tl}zerclrc t`r l}

    t`rkezrl} ! ! ? e ? + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 95

    9(0 ]erce je ltmle} je mlktr` hl kerm`jl h`mclh`a( ( ( ( ( ( ( ( ( ( ( ( ( 2?

    9(? _e}ukl j` jc}zrcoucml ` tl}zerclrc je e ? uzcacw`hjl l `zcyl

    TEZ_: + kljeal `( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 2:

    9(= _e}ukl j` jc}zrcoucml ` tl}zerclrc je ! ?

    e ?

    ! mlk `zcyl TEZ_:e ltmle} + kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 2>

    9(: Z`oea` je treml} t`r` `puc}cml j` ltml + kljeal o( ( ( ( ( ( ( ( ( ( >?

    9(5 _e}ukl t`r` ` `kl}zr` j` jc}zrcoucml ` tl}zerclrc je ! e ?!

    u}`hjl TEZ_: + kljeal j( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >=

    9(9 _e}ukl j` jc}zrcoucml ` tl}zerclrc je ! ! ? e ?! u}`hjl TEZ_:

    e nc}zlrcml je ltmle} + kljeal e( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( >>

    9(2 Z`oea` je treml} t`r` `puc}cml j` ltml + kljeal e( ( ( ( ( ( ( ( ( ( 34

    ~y

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    16/118

    9(> _e}ukl j`} jc}zrcoucmle} ` tl}zerclrc} t`r` l} kljeal} mlk yla`zcac+

    j`je chy`rc`hze }ckua`jl}( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 30

    9(3 _e}uaz`jl re}ukcjl j`} jc}zrcoucmle} ` tl}zerclrc jl} kljeal} mlk

    yla zcacj`je e}zlm}zcm` mlk j`jl} }ckua`jl}( ( ( ( ( ( ( ( ( ( ( ( ( ( 3?9(04 _e}ukl j`} jc}zrcoucmle} ` tl}zerclrc} t`r` l} kljeal} mlk yla`zcac+

    j`je chy`rc`hze uzcacw`hjl j`jl} jl kerm`jl ffh`hmecrl h`mclh`a( ( ( ( 3=

    9(00 _e}ukl j`} jc}zrcoucmle} ` tl}zerclrc} t`r` l} kljeal} mlk Yla`zcac+

    j`je E}zlm`}zcm` uzcacw`hjl j`jl} jl kerm`jl ffh`hmecrl h`mclh`a( ( ( 3=

    9(0? Z`oea` je treml} t`r` `puc}cml j` ltml ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 3:

    0 Treml} j` ltml TEZ_I34 e re}uaz`jl} NR! mlk y`alr jl `zcyl ml+

    hnemcjl + kljeal o( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 044

    ~yc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    17/118

    Ac}z` je ]kolal}

    .}Z!(((!}Z&c# + ]erce je y`alre} t`r` l `zcyl}! jl ch}z`hze Z `l Z&c6

    .}Z!(((!}Z&c# +]erce je y`alre} treyc}zl} t`r` l `zcyl jl ch}z`hze Z `l Z&c6

    O] + kljeal lu epu`ml je Oa`mf e ]mnlae}6

    NR + kljeal je Nuaa e Rncze6

    F + Treml je E~ermmcl6

    H.! ?# + Jc}zrcoucml Hlrk`a mlk kejc` e y`rchmc` ?6

    BC.`! o# + Jc}zrcoucml B`k` Chyer}` mlk t`rkezrl} ` e o6

    J(T( + Je}ycl T`jrl6

    ]B + @ablrczkl ]chbae Klye6

    IIO] + @ablrczkl Ilr`rj Icazerchb O`mf`rj ]`ktachb6

    Klj( + Kljeal6

    t.]Z!(((!]Z&c# + Jc}zrcoucml je trlo`ocacj`je mlhguhz` jl ch}z`hze Z `l Z&c6

    t.]Z!(((!]Z&c# + Jc}zrcoucml je trlo`ocacj`je mlhguhz` treyc}z` jl ch}z`hzeZ `l Z&c6

    t.O].]Z! j ; c#!(((!O].]Z&c!j;4## + Jc}zrcoucml je trlo`ocacj`je mlhguhz jetreml} O] jl ch}z`hze Z `l Z&c! mlk j;c!(((!4 `ze ` k`zurcj`je6

    t.NR.]Z! j ; c#!(((!NR.]Z&c! j ; 4## + Jc}zrcoucml je trlo`ocacj`je mlh+

    guhz` je treml} NR jl ch}z`hze Z `l Z&c! mlk j;c!(((!4 `ze ` k`zurcj`je6

    ~ycc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    18/118

    t.O].]Z! j ; c#!(((!O].]Z&c!j;4## + Jc}zrcoucml je trlo`ocacj`je mlhguhz jetreml} O] jl ch}z`hze Z `l Z&c! mlk j;c!(((!4 `ze ` k`zurcj`je! mlk y`alre}

    treyc}zl} t`r` l `zcyl6

    t.NR.]Z! j ; c#!(((!NR.]Z&c! j ; 4## + Jc}zrcoucml je trlo`ocacj`je mlh+guhz` je treml} NR jl ch}z`hze Z `l Z&c! mlk j;c!(((!4 `ze ` k`zurcj`je!

    mlk y`alre} treyc}zl} t`r` l `zcyl(

    ~yccc

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    19/118

    M`tzual 0

    Chzrljuml

    L zek` `olrj`jl tlr e}z` jc}}erz`ml zek mlkl lo gezcyl kl}zr`r pue ` chilrk`ml

    mlhzcj` ek treml} je ltmle} e }cbhcffm`zcyl `l }e e}zck`r ` yla`zcacj`je! }eg` ek uk

    kljeal pue zr`ze d je ilrk` chy`rc`hze lu jchkcm` hl zektl(

    L re}uaz`jl e}ter`jl mlk e}z` jc}}erz`ml e lozer e}zck`zcy`} k`c} tremc}`} t`r`

    l} t`rkezrl} e ilrhemer uk` ierr`kehz` treackch`r h` zlk`j` je jemc} l! t`r` }e

    `jpucrcr uk` ltml ek uk` jezerkch`j` j`z ( Uk` yew pue ` kezljlalbc` je

    tremcffm`ml ilrhemer uk` jc}zrcoucml je trlo`ocacj`je t`r` l} treml}(

    L zr`o`anl je}ehylaycjl zek }cbhcffm`zcy chuehmc` hl zr`o`anl je Tla}lh e

    Gln`hhe} .?449#! pue }ubere ` uzcacw`ml je treml} nc}zlrcml} je ltmle}! ek uk

    kljeal je yla`zcacj`je chy`rc`hze hl zektl( Jl tlhzl je yc}z` lhje ` yla`zcacj`je

    e zr`z`j` mlkl jchkcm`! ` chuehmc` e jl zr`o`anl je S`hb .033>#(

    @ kezljlalbc` uzcacw`j` h` e}zck`ml jl} t`rkezrl} e ` Chierehmc` O`se}c`h`

    e ` ]ckua`ml E}zlm}zcm`! `zr`ye} jl nc}zlrcml je treml} jl `zcyl e j` ltml( @

    e}zruzur` je}z` jc}}erz`ml mlh}c}ze ek `tre}ehz`r je ilrk` br`j`zcy` l} kljeal}

    uzcacw`jl}! eylauchjl jl k`c} }cktae} `l k`c} mlktae~l! zlz`acw`hjl ek mchml klj+

    eal} jcycjcjl} ek }emle}( T`r` m`j` uk jeae} }er re`acw`jl uk e~terckehzl `zr`ye}

    je j`jl} }ckua`jl}! mlh}zczuchjl je ber`ml je j`jl}! e}zck`ml je t`rkezrl}!

    treyc}l jl `zcyl logezl e tremcffm`ml je uk` ltml( @l ffh`a je}z` jc}}erz ml

    uk e~terckehzl mlk j`jl} lozcjl} jl kerm`jl ffh`hmecrl h`mclh`a! mlk ` `ml

    treierehmc`a hlkch`zcy` j` Tezrlor`}! e `tre}ehz`jl(

    @ tremcffm`ml t`r` l} kljeal} je}ehylaycjl} ilr`k re`acw`j`} uzcacw`hjl l klj+

    eal je Oa`mf e ]mnlae} .032=# + O]! t`r` uk mehrcl je yla`zcacj`je chy`rc`hze hl

    0

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    20/118

    zektl! e l kljeal je Nuaa e Rncze .03>2# + NR! t`r` uk meh rcl je yla`zcacj`je

    e}zlm}zcm`(

    L} jek`c} m`tzual} je}z` jc}}erz`ml e}zl lrb`hcw`jl} j` }ebuchze ilrk`( L

    m`tzual ? je}mreye l} kljeal} je O] e NR6 l m`tzual = `tre}ehz` l} mlhmeczl} jeChierehmc` E}z`z}zcm` O`se}c`h` e l} kezljl} mlktuz`mclh`c} uzcacw`jl}6 l} m`tzual}

    : e 5 chzrljuwek l} kljeal} t`r` yla`zcacj`je e ` uzcacw`ml j` chilrk`ml mlhzcj`

    hl} treml} j`} ltmle}! t`r` l} m`}l} chy`rc`hze} `l alhbl jl zektl e e}zlm}zcml}!

    re}temzcy`kehze6 l m`tzual 9 `tre}ehz` uk e}zujl je m`}l re`acw`jl mlk l `zcyl j`

    Tezrlor`}! t`r` l} kljeal} je}mrczl} hl m`tzual} : e 5 e l m`tzual 2 `tre}ehz` `

    mlhmau}l lozcj`! `}}ck mlkl }ube}zle} t`r` zr`o`anl} iuzurl}(

    ?

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    21/118

    M`tzual ?

    Trlme}}l je Zektl Mlhzhul

    E mlkuk uzcacw`r ` jciu}l ` }ebucr t`r` je}mreyer l} treml} je uk `zcyl(

    j~z ; jz & jz .?(0#

    E}z` jciu}l e jehlkch`j` Trlme}}l je Rceher Beher`acw`jl! Z}`s .?44?#! je+

    ycjl ` chmau}l jl} t`rkezrl} e `}}lmc`jl} `l Trlme}}l je Rceher ]cktae}! j`jl

    tlr jz! z`koek jczl Klyckehzl Orlhc`hl T`jrl( @ jc}mrezcw`ml j` jciu}l

    .?(0# i`w+}e heme}}rc`! tlc} lo}ery`mle} }l re`acw`j`} `teh`} ek ch}z`hze} jc}mrezl}

    je zektl( ]ehjl `}}ck! jeffhe+}e l Trlme}}l je Rceher Beher`acw`jl jc}mrezl(

    ~z ; z & z .?(?#

    0( 4;46

    ?( z ;

    z! lhje H.4! 0#! e

    =( z ilr chjetehjehze je g t`r` zljl g

    z(

    @ trckecr` mlhjcml jeffhe l trlme}}l hl ch}z`hze hual! ` }ebuhj` mlhjcml chjcm`

    pue z e hlrk`akehze jc}zrcoujl mlk kejc` werl e y`rchmc` z! z H.4! z#(@ zermecr` mlhjcml e uk` trltrcej`je je K`rfly! lhje j`jl l y`alr tre}ehze je

    z! pu`apuer chilrk`ml t`}}`j` jl trlme}}l e crreaey`hze t`r` l iuzurl z&a! mlk

    a 8 4( @ t`rzcr je}z` trltrcej`je yercffm`+}e pue l} chmrekehzl} }l chjetehjehze}(

    =

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    22/118

    ?(0 Trlme}}l je Czl

    @ z`~` je kuj`hm` e ` y`rc`ml ? ek uk Trlme}}l je Rceher Beher`acw`jl }l

    chy`rc`hze} `l alhbl jl zektl( Uk` ilrk` je e}zehjer e}ze kljeal e i`wer mlk

    pue e}ze} t`rkezrl} }eg`k iuhmle} jl trlme}}l e}zlm}zcml je}mrczl tlr ~z( E}z`

    beher`acw`ml remeoe l hlke je trlme}}l je Cz l! lhje z e ` retre}ehz`ml je uk

    Trlme}}l je Rceher ]cktae}(

    j~z ; .~z! z#jz & .~z! z#jz .?(=#

    ]ehjl `}}ck! ` jciu}l `tre}ehz` `hzerclrkehze ek .?(0# tlje }er chzertrez`j` mlkl

    uk m`}l t`rzcmua`r je uk Trlme}l je Czl! mlk t`rkezrl} mlh}z`hze}( C}zl e uzca

    t`r` }e lozer l treml je uk jercy zcyl ffh`hmecrl! lhje i`w+}e u}l jl Mamual je

    Czl( Ek uk trckecrl klkehzl jeffhe+}e ` iuhml B! jcierehmyea ek ~z e z! ehzl!

    ` t`rzcr j` E~t`h}l je Z`salr! lozek+}e7

    B ;B

    ~~ &

    0

    ?

    ?B

    ~?.~#? &

    ?B

    ~z~z &

    0

    ?

    ?B

    z?.z# & ((( .?(:#

    Zlk`hjl ` yer}l jc}mrezcw`j` jl Trlme}}l je Czl! ek .?(?#! jezerkch`+}e .~#?7

    .~#? ; ?.z#? & ??z & ?.#

    =,? ; ??z & N.z# .?(5#

    Lhje N.z# jehlz` l} zerkl} je k`clr lrjek je z( Zlk`hjl+}e l ackcze z 4!l} zerkl} je k`clr lrjek }l je}mlh}cjer`jl} e lozek+}e7

    E.??z# ; ?z .?(9#

    Y `r.??z# ; ?:.z#

    ? .?(2#

    Tlc}! E.:# ; =! t`r` uk` y`rcyea hlrk`a t`jrl( @} ju`} trltrcej`je} `mck`

    kl}zr`k pue ??z mlhyerbe t`r` uk` pu`hzcj`je ?z! pu`hjl z 4! mlh+

    }epuehzekehze je .?(5#7

    .~#? ?jz! pu`hjl z 4 .?(>#

    :

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    23/118

    @ t`rzcr je}}e} re}uaz`jl} }uo}zczuchjl+l} h` epu`ml ?(: jezerkch`+}e jB

    jB ;B

    ~j~ &

    B

    zjz &

    0

    ?

    ?B

    ~??jz

    ;B

    ~ .~z! z# &

    B

    z &

    0

    ?

    ?B

    ~? .~z! z#?

    jz &

    B

    ~ .~z! z#jz .?(3#

    L re}uaz`jl ek .?(3# e mlhnemcjl mlkl Aek` je Czl(

    ]ehjl ]z l treml jl `zcyl! uk trlme}}l e}zlm}zcml je zektl mlhzhul jeffhcjl ek

    z V4!# e zlk`hjl l} y`alre} .]z! z# ; ]z e .]z! z# ; ]z! t`r` l} t`rkezrl}jl Trlme}}l je Czl! je `mlrjl jeffhcjl ek .?(=#!

    j]z ; ]zjz & ]zjz .?(04#

    lhje e }l mlh}z`hze}( L Trlme}}l je Czl ek .?(04#! e jehlkch`jl Klyckehzl

    Orlhc`hl Belkezrcml(

    @tacm`hjl l Aek` je Czl! .?(3#! t`r` jezerkch`r l kljeal je zektl mlhzhul j`

    iuhml B.]z! z# ; ah.]z#!

    B

    ]z;

    0

    ]z!

    B

    z; 4!

    0

    ?

    ?B

    ]?z;

    0

    ?

    0

    ]?z

    j ah.]z# ;

    0]z

    ]z & 0?

    0

    ]?z?]?z

    jz & 0

    ]z]zjz

    ;

    ?

    ?

    jz & jz .?(00#

    E}}e re}uaz`jl kl}zr` pue j ah.]z# e uk Trlme}}l je Rceher Beher`acw`jl! mlk

    t`rkezrl} . ?,?#jz e ?jz(@ jc}mrezcw`ml jl trlme}}l re}uaz`hze ek .?(00# cktacm` ek chmrekehzl}!

    ah.]z# ;

    ?

    ?

    z &

    zz .?(0?#

    L trlme}}l ber`jlr jl} treml} tlje }er lozcjl tea` e~tlhehmc`ml je .?(0?#(

    ]z&z ; ]z e~t

    ?

    ?

    z &

    zz

    .?(0=#

    ?(? Ltmle} e l Kljeal je Oa`mf `hj ]mnlae} + O]

    E}z` }eml je}mreye ` `hac}e re`acw`j` t`r` jezerkch`r ` epu`ml jcierehmc`a e}+

    zlm}zcm` pue je}mreye l kljeal je tremcffm`ml je ltmle} je Oa`mf e ]mnlae}( @

    5

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    24/118

    jeffhcml je uk` ltml tlje }er j`j` mlkl uk }eburl }lore uk jezerkch`jl ch+

    ye}zckehzl( Mlkl pu`apuer }eburl e~c}ze uk tr`wl je y`acj`je! jczl `puc zektl

    `ze ` k`zurcj`je! pue e `mlrj`jl ehzre l Zczua`r e l A`hm`jlr( E~c}ze uk trekcl!

    y`alr t`bl tea` ltml! e e~c}ze uk y`alr remeocjl ek m`}l je }chc}zrl! jczl treml jee~ermmcl(

    L Zczua`r e `pueae pue `jpucrc ` ltml e l A`hm`jlr e `pueae pue liereme ` ltml

    hl kerm`jl( O`}cm`kehze e~c}zek jlc} zctl} je ltmle}! `} je yehj` e `} je mlktr`(

    L ilml je}ze zr`o`anl }l `} ltmle} je mlktr`! pue hl Or`}ca }l hlrk`akehze

    mlkermc acw`j`} `zr`ye} jl kljeal eurlteu! lhje ` e~emuml tlje }er re`acw`j`

    }lkehze h` j`z` jl }eu yehmckehzl(

    Ltml je Mlktr`7 L A`hm`jlr,Chye}zcjlr `l `jpucrcr e}ze zctl je ltml tl}}uc

    l jcreczl je mlktr`r l `zcyl! teal treml ff~`jl! h` j`z` jl t`b`kehzl jl trekcl(

    Hl n ` lorcb`ml je e~ermer ` ltml! pu`hjl e}z` mneb` `l }eu yehmckehzl(

    M`oe `l trltrcezrcl j` ke}k` jemcjcr }e e rehzyea lu chjcierehze ` e~emuml!

    chjcierehze mlh}cjer`hjl pue g lmlrreu l treguwl mz! treml t`bl tea` ltml( L

    Chye}zcjlr! pue e}z hl ch}z`hze je zektl z! tlje mlktr`r ` ltml tlr uk trekcl

    mz t`r` uk `zcyl ] pu`apuer! mlz`jl d ]z h` j`z` j` `puc}cml ` ltml( E}z`

    ltml j`r `l chye}zcjlr l jcreczl je `jpucrcr l `zcyl ] d uk y`alr F! h` j`z` je

    yehmckehzl jeffhcj` mlkl Z! lhje l zektl jemlrrcjl e je Zz jc`}( ]e F&mz 8 ]Zhl ch}z`hze Z! lmlrre aumrl( ]ehjl `}}ck! t`r` e}z`oeaemer uk y`alr cje`a t`r` l

    treml! e heme}}rcl `h`ac}`r l} mehrcl} h` j`z` je yehmckehzl }ek l treml mz t`bl

    tea ltml(

    c# ]e ]Z 8 F! t`r` ]ZF 8 4! e chzere}}`hze mlktr`r ]Z teal treml je e~ermmclF! lu }eg`! e~ermer ` ltml je mlktr`! tlc} l `zcyl y`alrcwlu ek rea`ml `l

    zektl z6

    cc# ]e ]Z ; F! t`r` ]Z F ; 4! e chjcierehze `jpucrcr ]Z teal treml F6

    cc# ]e ]Z 1 F! t`r` ]Z F 1 4! hl e chzere}}`hze mlktr`r ]Z teal treml F! lkeanlr e mlktr`r l `zcyl jcrezl jl kerm`jl(

    T`r` tljer jemcjcr je `mlrjl mlk c#! cc# lu ccc# mlh}cjer +}e pue l treml j` ltml

    .trekcl# e}z `}}lmc`jl ` iuhml k`~.]ZF! 4#( @ t`rzcr jc}zl! l treml t`bl t`r``puc}cml je uk` ltml ek uk ch}z`hze z! e j`jl teal y`alr e}ter`jl j` iuhml

    9

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    25/118

    kehmclh`j`! ek rea`ml ` `zcyl ]Z! zr`wcjl d y`alr tre}ehze! tlr uk` z`~` je gurl}

    r7

    mz ; evr.Zz#{EVk`~.]ZF! 4#[ .?(0:#lhje7 E]ZVk`~.]ZF! 4#[ ;

    F

    .]Z F#t.]Z#j]Z

    @ cjec` jl} kljeal} je tremcffm`ml je ltmle} e }ektre e~talr`r `} rea`mle} ehzre

    l kerm`jl je `mle}! je ltmle} e je zzual} .}ek rc}ml#( Tlr e~ektal! l treml je

    uk` ltml je mlktr` ml}zuk` }uocr! pu`hjl }eu `zcyl y`alrcw`+}e! ` remtrlm` e

    yerj`jecr ( C}zl lmlrre tlc}! ` kejcj` pue l treml je uk` `ml }loe! l aumrl jl

    tl}}yea e~ermmcl je uk` m`aa e m`j` yew k`clr(@}}ukchjl l m`}l je}mrczl ek Rcaaklz .0335#! `} }ebuchze} nctlze}e} }l

    heme}}rc`} t`r` ` ilrkua`ml jl kljeal O](

    L treml jl `zcyl e je}mrczl tlr uk Klyckehzl Orlhc`hl Belkezrcml! yer.?(04#6

    @ z`~` je gurl} r acyre je rc}ml e ` yla`zcacj`je }l mlh}z`hze}6

    Hl e~c}ze mu}zl} `}}lmc`jl} `l }e jcyer}cffm`r uk tlrzilacl6

    L `zcyl hl t`b` jcycjehjl} jur`hze l zektl je ycj` j` ltml6

    Hl e~c}ze tl}}cocacj`je je `roczr`bek! lu }eg`! t`r` pu`apuer tlrzcilacl acyreje rc}ml! l rezlrhl lozcjl e l ke}kl6

    @ heblmc`ml jl `zcyl tlje }er re`acw`j` je ilrk` mlhzhu`6

    Yehj`} je murzl tr`wl }l terkczcj`} e l} `zcyl} }l jcyc}yec}( Tlje+}e yehjerlu mlktr`r pu`apuer pu`hzcj`je je uk jezerkch`jl `zcyl .hl heme}}`rc`+

    kehze uk chzecrl# e heblmc`r `zcyl} pue hl }e tl}}u`(

    Bzz

    & r]zBz]z

    &0

    ??]?z

    ?Bz]?z

    ; rBz! lhje7 Bz ; B.]z! z#! .?(05#

    Ek 032=! Oa`mf e ]mnlae} lozcyer`k }ume}}l ek re}layer ` epu`ml jciereh+

    mc`a `mck`! lozehjl uk` ilrkua`ml `h`azcm` t`r` l }eu kljeal je tremcffm`ml

    je ltmle}( .Z}`s! ?44?#

    2

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    26/118

    @ }lauml ilc lozcj` uzcacw`hjl l Aek` je Czl! }ehjl Bz l treml jl jercy`zcyl e

    r ` z`~` je gurl} acyre je rc}ml( Tlrek! ` }lauml jetehje j` mlhjcml je irlhzecr`

    ` }ebucr7

    BZ ; k`~.]ZF! 4# .?(09#

    ?(?(0 @ Nctlze}e je Kuhjl _c}ml+Heuzrl

    Ek kljeal} je ffh`hm`}! ` nctlze}e je _c}ml+Heuzrl }cbhcffm` pue hl }e mlh}cjer`

    treierehmc`} `l rc}ml( Ek luzr`} t`a`yr`}! }er `ye}}l lu i`ylryea `l rc}ml hl `iez`

    ` }lauml j` epu`ml .?(05#( @ t`rzcr jc}}l l} }ebuchze} re}uaz`jl} }l yacjl}7

    L y`alr e}ter`jl mlkl rezlrhl! t`r` pu`apuer y`alr }ebur`jl! e ` z`~` je gurl}acyre je rc}ml r6

    L y`alr tre}ehze! t`r` pu apuer u~l je m`c~`! tlje }er lozcjl `zr`ye} jlje}mlhzl jl y`alr e}ter`jl! uzcacw`hjl ` z`~` je gurl} acyre je rc}ml r(

    @ Ilrkua`ml jl Kljeal Oa`mf `hj ]mnlae}

    @ t`rzcr j` iuhml .?(09#! zlk`+}e l y`alr e}ter`jl ek rea`ml d ]Z( E}z` e}ter`hm`

    e l treml j` ltml je mlktr` h` j`z` jl }eu yehmckehzl7

    E]Z Vk`~.]Z F! 4#[

    L treml j` ltml je mlktr` ek uk ch}z`hze z pu`apuer! mlk z 1 Z! e lozcjl `

    t`rzcr jl je}mlhzl ffh`hmecrl! uzcacw`hjl uk` z`~` je gurl} acyre je rc}ml r7

    mz ; e~tVr.Z z#[E]Z Vk`~.]ZF! 4#[ .?(02#

    @ t`rzcr j` epu`ml .?(0?# e uzcacw`hjl ` nctlze}e je kerm`jl acyre je rc}ml! `

    jc}zrcoucml t`r` l alb`rczkl jl treml jl `zcyl! ek }u` j`z` je yehmckehzl e j`j`

    tlr7

    ah.]Z# H

    ah.]z# & .r ?

    ?#.Z z#! ?.Z z#

    .?(0>#

    Jeffhchjl b.]Z# ` iuhml jeh}cj`je je trlo`ocacj`je je ]Z! ehzl l treml je

    uk` ltml je mlktr` ek .?(02# e7

    >

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    27/118

    mz ; e~tvr.Z z#{F

    .]ZF#b.]Z#j]Z

    I`wehjl ~ ; ah.]Z#( Tea` kuj`hm` je y`rcyea e uzcacw`hjl b.]Z#j]Z ; i.~#j~!}ehjl i.~# ` iuhml jeh}cj`je je trlo`ocacj`je je ~(

    mz ; er.Zz#

    F

    .]Z F#b.]Z#j]z

    ; er.Zz#ah.F#

    .e~ F#i.~#j~

    ; er.Zz#

    ah.F# e~

    i.~#j~ F

    ah.F# i.~#j~

    .?(03#

    @ }lauml je .?(03# }er lozcj` ek ez`t`}( ]ehjl ` jc}zrcoucml je ah.]Z#! j`j`

    tlr .?(0>#! ` chzebr`a jl }ebuhjl zerkl je .?(03# rejuw+}e d7

    ah.F#

    i.~#j~ ; 0 ah.F#

    i.~#j~

    ; 0 I

    ah.F#

    .?(?4#

    lhje! I.(# e iuhml je jc}zrcoucml `mukua`j` t`r` ~(

    Je `mlrjl mlk Z}`s .?44?#! }`oe+}e pue ` jc}zrcoucml `mukua`j` je ~ `y`ac`j`

    ek ah.F#! e uk` jc}zrcoucml hlrk`a t`jrl `mukua`j`! ! `y`ac`j` ek j0! lhje7

    j0 ; ah.F# ah.]z# .r ?,?#.Z z#

    Z z;

    ah.]z,F# & .r ?,?#.Z z#

    Z z

    ]ehjl `}}ck! ah.F#

    i.~#j~ ; 0 I

    ah.F#

    ; 0 .j0# ; .j0#

    T`r` ` chzebr`a reierehze `l trckecrl zerkl j` epu`ml .?(03#! tlje+}e e}mreye+a`

    mlkl7

    ah.F#

    0??.Z z# e~t

    ~

    V~

    ah.]z#

    .r

    ?,?#.Z

    z#[?

    ??.Z z#

    j~

    3

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    28/118

    lhje ` t`rmea` jehzrl j` iuhml e~tlhehmc`a! tlje }er }cktacffm`j` ek7

    ; ~

    ~

    ah.]z# &

    r ?,?.Z z#?

    ??.Z z#

    ;

    ~ ah.]z# & r & ?,?.Z z#???.Z z# & r.Z z# & ah.]z#

    mlh}epuehzekehze ` trckecr` chzebr`a je .?(03# zlrh`+}e7

    er.Zz#ah.F#

    0.??.Z z## e~t

    V~ .ah.]z# & .r &

    ?,?#.Z z##[???.Z z#

    j~

    @}}ck mlkl ieczl t`r` ` }ebuhj` chzebr`a! jeffhe+}e l re}uaz`jl ek iuhml je

    uk` jc}zrcoucml hlrk`a t`jrl `mukua`j`! `y`ac`j` ek j?! lhje7

    j? ;ah.]z,F# .r & ?,?#.Z z#

    Z zalbl! l y`alr t`r` l treml je uk` ltml je mlktr` e j`jl tlr .?(?0#! mlhnemcjl

    mlkl kljeal je Oa`mf e ]mnlae}(

    mz ; er.Zz#

    ]ze

    r.Zz#.j?# F.j0#

    O]z ; ]z.j?# Fer.Zz#

    .j0# .?(?0#

    ?(= L Kljeal je Nuaa Rncze + NR

    L kljeal O] uzcacw` ` trekc}}` je yla`zcacj`je chy rc`hze `l alhbl jl zektl( Ek

    }eu zr`o`anl! Nuaa .03>2#! trltl} uk` e}zruzur` e}zlm}zcm` t`r` ` yla zcacj`je!

    yc}`hjl lozer keanlre} re}uaz`jl} t`r` tremcffm`ml je uk` ltml( T`r` c}zl trltl}

    ` jciu}l ` }ebucr7

    j]z ; ]zjz &

    Yz]zjz

    jYz ; Yzjz & Yzjwz .?(??#

    lhje jz e jwz }l trlme}}l} je Rceher chjetehjehze}(

    Je `mlrjl mlk Nuaa .03>2#! ` }lauml jl }c}zek` je epu`mle} `mck`! ilc lozcj`

    ` t`rzcr j` re}lauml j` epu`ml jcierehmc`a7

    i

    z&

    0

    ?

    c!g

    cgcg?i

    cg ri ;

    c

    ci

    cVc & . r#[ .?(?=#

    04

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    29/118

    Lhje i e l treml je }ebur`hm` t`r` l jercy`zcyl06 c e l `zcyl6 c l je}ycl t`jrl

    ch}z`hzhel t`r` c6 cg e mlrrea`ml ch}z`hzhe` ehzre c e g6 g e e}t`ml je e}z`jl

    hl lo}eryyea! lu }eg`! ` yla`zcacj`je e}zlm}zcm`6 c e ` z`~` je je}alm`kehzl jl

    `zcyl6 c e uk yezlr je rebre}}lre} ehzre l rezlrhl jl `zcyl e ` m`rzecr` je kerm`jl6 e l yezlr e}ter`jl je rezlrhl} ch}z`hzhel} jl `zcyl e r e l yezlr mlk l} eaekehzl}

    acyre} je rc}ml(

    E tl}}yea e}mreyer ` epu`ml .?(?=# j` }ebuchze ilrk`7

    i

    z&

    0

    ?

    ?]?

    ?i

    ]?& ?=]

    ?i

    ]Y& ?Y?

    ?i

    Y?

    ri ; r]i

    ] ? ]

    Y.?(?:#

    @}}uke+}e ; 4! lu }eg`! hl n mlrrea`ml ehzre ] e Y! c}}l e epucy aehze `

    `ffrk`r pue hl n `a`y hm`bek( Uk` }lauml `h`azcm` t`r` .?(?:#! hl m`}l je

    uk` ltml je mlktr` jl zctl eurltec`! tlje }er lozcj` uzcacw`hjl ` nctlze}e je

    `y`ac`ml acyre je rc}ml( Mlkl .?(?:# e }u`} mlhjcmle} je irlhzecr` hl jetehjek

    j`} treierehmc`} `l rc}ml jl chye}zcjlr! tlje+}e `}}ukcr t`r` l mamual j` ltml

    heuzr`acj`je! `}}ck mlkl ieczl mlk l kljeal O]( Jeffhchjl mz mlkl l y`alr tre}ehze

    jl y`alr e}ter`jl t`r` i! je}mlhz`jl je uk` z`~` je gurl} acyre je rc}ml! r( L treml

    j` ltml e j`jl tlr7

    mz ; er.Zz#

    i.]Z! YZ! Z#t.]Zq]z! Yz#j]Z .?(?5#

    @ jc}zrcoucml mlhjcmclh`a je ]Z jetehje je `kol} l} trlme}}l}! ] e Y( T`r`

    acj`r mlk e}z` jetehjehmc` Nuaa .03>2#! uzcacwlu l i`zl je pue! j`j` zre} y`rcyec}

    `ae`zlrc`} ^! S e W! `} iuhmle} je jeh}cj`je je trlo`ocacj`je mlhjcmclh`c} tljek

    }er e}mrcz`} mlkl7

    t.~qs# ;

    t.~qw#t.wqs#jw

    Jeffhchjl ` y`rchmc` kejc` }lore l zektl je ycj` jl jercy`zcyl Y mlkl

    Y ;

    0

    Z z Z

    z Ycjc .?(?9#

    0i e iuhml k`~.]Z F#

    00

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    30/118

    @ jc}zrcoucml je ]Z tlje }er e}mrcz` mlkl7

    t.]Z

    qYz# ; t.]Zq

    Y#t. Y

    qYz#j Y .?(?2#

    @ jetehjehmc` }lore ]z e~c}ze! k`} ilc lkczcj` t`r` }cktacffm`r ` hlz`ml( @l

    }uo}zczucr .?(?2# ek .?(?5# }e lozek7

    mz ; er.Zz#

    i.]Z! YZ! Z#t.]Zq Y#t. YqYz#j]Zj Y .?(?>#

    _elrb`hcw`hjl l} zerkl} e tl}}yea e}z`oeaemer uk` rea`ml jcrez` mlk ` e~+

    tre}}l iemn`j` t`r` ` epu`ml je O]7

    mz ;

    er.Zz#

    i.]Z! YZ! Z#t.]Zq Y#j]Z

    t. YqYz#j Y .?(?3#

    ;

    O].]z! YqYz#t. YqYz#j Y

    Je `mlrjl mlk Nuaa .03>2#! ` epu`ml .?(?3# hl `tre}ehz` }lauml `h`azcm`(

    ]ehjl `}}ck! l} re}uaz`jl} t`r` l treml je uk` ltml tlr NR }l lozcjl} uzc+

    acw`hjl kezljl} mlktuz`mclh`c}! ek t`rzcmua`r ]ckua`ml je Klhze M`ral( @ }ck+

    ua`ml uzcacw` `} jc}mrezcw`mle} ek .?(=0#! t`r` l }c}zek` `tre}ehz`jl ek .?(??#!

    e}ze} re}uaz`jl} }l lozcjl} ` t`rzcr jl Aek` je Czl(

    Mamual jl Treml NR Yc` ]ckua`ml je Klhze+M`ral

    ]z ; ]z0 e~t

    .r Yz0,?#z &

    Yz0zz

    .?(=4#

    Yz ; Yz0 e~t

    . ?,?#z &

    zz

    ! lhje7 z!z H.4! 0# .?(=0#

    T`r` jezerkch`r uk treml NRz e heme}}rcl ber`r y`alre} t`r` ` yla`zcacj`je je

    ilrk` czer`zcy`! je}je l ch}z`hze z `ze l yehmckehzl j` ltml( C}zl e ieczl `zr`ye} j`

    epu`ml .?(=0#! pue e ` jc}mrezcw`ml j` jciu}l .?(??#( Je tl}}e jl} y`alre} ber`jl}!

    m`amua +}e ` yla zcacj`je kejc` jl ch}z`hze z `l yehmckehzl j` ltml! ` t`rzcr j`

    epu`ml .?(=?#( E}ze re}uaz`jl e l epucy`aehze jc}mrezl t`r ` chzebr a `tre}ehz`j`

    ek .?(?9#! ehz`l m`amua`+}e l treml O]! uzcacw`hjl l y`alr Yz mlkl yla`zcacj`je( L

    0?

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    31/118

    trlme}}l e retezcjl H yewe} e l treml NRz e m`amua`jl ` t`rzcr j` kejc` je m`j`

    O]z lozcjl( L m`amual yc` ]ckua`m`l je Klhze M`ral ber` uk` jc}zrcoucm`l je

    trlo`ocacj`je t`r` NRz(

    Yz ;0

    Z zZc;z

    Yc! .?(=?#

    lhje Z e ` j`z` je yehmckehzl j` ltml(

    E}zck`r l} t`rkezrl} j`} epu`mle} .?(=4# e .?(=0# hl e z`rei` zrcyc`a( Uk`

    }lauml ilc uzcacw`r uk` }cktacffm`ml j` jciu}l .?(??# e mlh}epuehzekehze uk`

    jc}mrezcw`ml k`c} }cktae}! l m`tzual 5 `olrj` keanlr e}z` pue}zl(

    Hl m`tzual }ebuchze }erl chzrljuwcjl} `abuh} mlhmeczl} je chierehmc` e}z`z}zcm`

    o`se}c`h` e l} `ablrczkl} u}`jl} h` e}zck`ml jl} t`rkezrl} jl} kljeal} `tre+

    }ehz`jl}(

    0=

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    32/118

    M`tzual =

    Chierehmc e Mlktuz`ml

    O`se}c`h`

    He}ze m`tzual `tre}ehz`+}e `} zemhcm`} o`}e`j`} ek kezljl} o`se}chl}! pue yek

    `tre}ehz`jl re}uaz`jl} }`zc}i zlrcl} ek kljeal} ffh`hmecrl}! trchmct`akehze `zr`ye}

    jl} kezljl} je }ckua`ml je Klhze M`ral yc` M`jec`} je K`rfly + KMKM! ek

    e}temc`a `} zemhcm`} Kezrltlac} N`}zchb} e Bcoo}( Z`koek }erl `olrj`jl} `abuh}

    iuhj`kehzl} je Chierehmc` O`se}c`h` e Kljeal} Jchkcml}(

    =(0 Zelrek` je O`se}

    Je `mlrjl mlk Kcblh e B`kerk`h .0333#! }eg` uk` pu`hzcj`je je chzere}}e

    je}mlhnemcj` ! terzehmehze `l e}t`ml `kl}zr`a ! lhje tlje }er uk e}m`a`r!

    uk yezlr lu uk` k`zrcw( ]eg` J ` retre}ehz`ml t`r` ` chilrk`ml nc}zlrcm` jl

    t`rkezrl ! }ehjl e~tre}}` je ilrk` trlo`oca}zcm` tlr t.

    qJ#(

    Hl }ehjl }uffmcehze ` chilrk`ml mlhzcj` ek J! i`w+}e u}l j` e~terc+

    kehz`ml uzcacw`hjl l yezlr lo}eryyea ^! pue e}z rea`mclh`jl d ( @tl} lo+

    }ery`r ^ l mlhnemckehzl treycl jl t`rkezrl ! retre}ehz`jl tlr J! t`}}` ` }er

    J ; Jv^ ; ~{! lhje J e uk }uomlhguhzl je J! uk reffh`kehzl ` re}teczl j`chilrk`ml(

    @ chilrk`ml je e re}ukcj `zr`ye} je t.q~! J#! e ` rea`ml e~c}zehze ehzree}}e} zerkl} e retre}ehz`j` ` }ebucr7

    0:

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    33/118

    t.q~! J# t.~q! J#t.qJ#! .=(0#

    E}ze re}uaz`jl e mlhnemcjl mlkl zelrek` je O`se} e tlje }er ree}mrcz` je uk`ilrk` k`c} }cktae}!

    t.q~# t.~q#t.#

    uk` yew pue ` jetehjehmc` ek J e uk i`zlr mlkuk d zljl} zerkl}(

    ]ehjl7

    t.# ` jc}zrcoucml ` trclrc! ` retre}ehz`ml trlo`oca}zcm` treyc` ` re}teczl jlt`rkezrl 6

    t.~q# ` iuhml je yerl}}ckcan`hm`! mlk ` chilrk`ml mlhzcj` ek y`alre} lo+}eryyec} rea`mclh`jl} `l t`rkezrl6

    t.q~# ` jc}zrcoucml ` tl}zerclrc! ` retre}ehz`ml trlo`oca}zcm` je ! `tl} `chilrk`ml lo}eryyea(

    @ epu`ml .=(0# e y`acj` t`r` y`alre} jc}mrezl}! mlhzhul}! e}m`a`re}! yezlrc`c} e

    k`zrcmc`c}( Je i`zl! l zelrek` je O`se} ilrheme uk` rebr je `zu acw`ml t`r` `}

    trlo`ocacj`je} ehylayehjl l t`rkezrl ! chcmc`hjl ek t.# e ehzl lozehjl t.q~#!jeffhchjl `}}ck `} jc}zrcoucmle} ` trclrc e ` tl}zerclrc! re}temzcy`kehze(

    Uk luzrl `}temzl pue }ebue jl} mamual} `tre}ehz`jl}! e ` kezljlalbc` `u+

    zlkzcm` t`r` re`acw`r treyc}le}! lhje S e retre}ehz`jl trlo`ocac}zcm`kehze tlr

    t.sq#(

    t.sq~# ;

    t.s! q~#j

    ;

    t.sq#t.q~#j

    @ uazck` cbu`aj`je jeye+}e ` chjetehjehmc` ehzre ^ e S mlhjcmclh`jl} `l

    t`rkezrl (

    05

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    34/118

    =(? Klhze M`ral Yc` M`jec` je K`rfly

    @ cjec` jl} Kezljl} Klhze M`ral yc` M`jec`} je K`rfly mlh}c}ze ek lozer uk`

    `kl}zr` j` jc}zrcoucml ` tl}zerclrc e m`amua`r e}zck`zcy`} `kl}zr`c} j`} m`r`m+

    zer}zcm`} je}z` jc}zrcoucml( L} kezljl} k`c} jciuhjcjl} }l7 Kezrltlac}+N`}zchb} e

    Bcoo}! lhje l uazckl tlje }er je}mrczl mlkl uk m`}l t`rzcmua`r jl trckecrl( @ trl+

    tl}z` iuhj`kehz`a! t`r` `kol} l} kezljl}! mlh}c}ze ek }ckua`r uk t`}}ecl `ae`zlrcl

    je ! hl e}t`ml `kl}zr`a ! pue mlhycrg` t`r` uk` jc}zrcoucml e}z`mclhrc`! je ch+

    zere}}e t`r` l trloaek`! k`clre} jez`ane} tljek }er yc}zl} ek B`kerk`h e Alte}

    .?449# e Kcblh e B`kerk`h .0333#(

    =(= Kezrltlac} N`}zchb}

    L `ablrczkl je Kezrltlac}+N`}zchb} ilc chzrljuwcjl ek Kezrltlac} ez `aa( .035=# e

    beher`acw`jl ek N`}zchb} .0324#( ]eu iuhmclh`kehzl mlh}c}ze h` ber`ml je y`alre}

    `ae`zlrcl} je uk` jc}zrcoucml je trlo`ocacj`je trltl}z` p.#! mlkl uk` `azerh`+

    zcy`! yc}zl pue e kuczl jcimca `kl}zr`r jcrez`kehze j` jc}zrcoucml je chzere}}e t.#(

    L} y`alre} ber`jl} }l `meczl} ` t`rzcr je uk` trlo`ocacj`je T(

    L `ablrczkl tlje }er cktaekehz`jl j` }ebuchze ilrk`7

    0( @zrcou` uk y`alr chcmc`a t`r` .4#! c ; 46

    ?( T`r` c 0! `kl}zre p.qc0#6

    =( Bere u U.4! 0#! }e T.c! c&0# 8 u! i`m` c ! m`}l mlhzrrcl

    c

    c06

    :( I`m` c ; c & 0 e ylaze t`r` l zek ? 6

    5( _etezcr `ze ` mlhyerbehmc`(

    L t`}}l `zu`a e retre}ehz`jl tlr c e l t`}}l }ebuchze tlr c & 0! hlze pue! `

    jc}zrcoucml trltl}z` ber` m`hjcj`zl} ` }uo}zczucr ` tl}cml c & 0( L y`alr ber`jl

    e `meczl }e kejc`hze l re}uaz`jl lozcjl `zr`ye} j` y`rcyea U! mlk jc}zrcoucml je

    trlo`ocacj`je uhcilrke ehzre 4 e 0! e ` trlo`ocacj`je je `mecz`ml jl `ablrczkl T

    09

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    35/118

    e~tre}}` tlr7

    T.c! c&0# ; kch

    0!

    t.c&0#p.cqc&0#t.c#p.c&0qc#

    .=(?#

    E tl}}yea uzcacw`r pu`apuer jc}zrcoucml mlkl trltl}z`( Tlrek uk` e}mlan`

    ch`jepu`j` cktacm` ek uk` m`jec` mlk mlhyerbehmc` aehz`! lu hl mlhyerbehze!

    jeycjl `l `azl hjcme je regecml jl zek =( E mlkuk uzcacw`r jc}zrcoucmle} pue

    muor`k` jc}zrcoucml je chzere}}e t`r` mlhzlrh`r e}ze trloaek`(

    =(: @kl}zr`jlr je Bcoo}

    L `ablrczkl je Bcoo} ilc trltl}zl tlr Bek`h e Bek`h .03>:#! k`} ilc mlk l

    zr`o`anl je Beai`hj e ]kczn .0334# pue t`}}lu ` }er tltua`r( E uk m`}l t`rzcmua`r

    t`r` l Kezrltlac} + N`}zchb}! lhje l y`alr ber`jl mlkl trltl}z` e }ektre `meczl(

    ]eg` t.fqf# jeffhcj` mlkl jc}zrcoucml mlhjcmclh`a mlktaez` t`r` f! lhjef ; .4! 0!(((!f0! f&0!(((!t#! e l mlhguhzl je t`rkezrl} ehylaycjl}! ` kehl}

    je f( @}}ukchjl pue }eg` tl}}yea `kl}zr`r y`alre} j` jc}zrcoucml mlhjcmclh`a

    mlktaez` je f! l `ablrczkl e chcmc`jl je ilrk` `ae`zlrc` 4 ; .

    .4#0 !(((!

    .4#t #( Ehzl

    `kl}zr`+}e t..0#q.4##! t..?#q.0## e `}}ck tlr jc`hze! `ze pue ` m`jec` ber`j` e}zeg`ek epucaorcl(

    L `ablrczkl tlje }er cktaekehz`jl j` }ebuchze ilrk`7

    0( @zrcou` y alre} t`r` 4 ; ..4#0 !(((!

    .4#t #6

    ?( T`r` c 0! ` `kl}zre .c#f t..c#f q.c0#f #! h` ke}k` czer`ml i`m` `zu`acw`mlje .c#f ` t`rzcr je

    .c#f g `kl}zr`jl7

    .c#0 t.0q.c0#? ! .c0#= !(((!.c0#t #6

    .c#? t.?q.c0#0 ! .c0#= !(((!.c0#t #6

    .c#= t.0q.c0#0 ! .c0#? !(((!.c0#t #6(((

    .c#t t.0q.c0#0 ! .c0#? !(((!.c0#t0 #6

    =( I`m` c ; c & 0 e ylaze t`r` l zek ?6

    :( _etezcr `ze `zchbcr ` mlhyerbehmc`(

    02

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    36/118

    =(5 Kljeal} Jchkcml}

    E}z` }eml i`r uk` chzrljuml }lore l} kljeal} jchkcml} ache`re}! je `mlrjl mlk

    ` `olrj`bek o`se}c`h` `tre}ehz`j` ek Re}z e N`rrc}lh .0332#( L kljeal e jeffhcjl

    tlr ju`} epu`mle} ` }`oer7

    Sz t.szqz! #z t.zqz0! #

    lhje Sz e l yezlr je lo}ery`mle}! z e l yezlr je e}t`ml je e}z`jl}! l yezlr je

    t`rkezrl} ff~l}! lu nctert`rkezrl}! e z e l chjcm`jlr zektlr`a( Mlk ` eylauml

    jl zektl! zlj` ` chilrk`ml reaey hze t`r` treyer l iuzurl e remeocj` e tlje }eruzcacw`j` h` reyc}l e mrzcm` jl kljeal(

    @ k`clr jcffmuaj`je h` uzcacw`ml je kljeal} jchkcml} e ` e}zck`ml jl ye+

    zlr je e}t`ml je e}z`jl}! pue `ukehz`k je `mlrjl mlk l hukerl je lo}ery`mle}(

    Jeycjl ` br`hje m`t`mcj`je mlktuz`mclh`a `zu`a! ` `olrj`bek o`se}c`h` zek }cjl

    uzcacw`j` `kta`kehze! tlc} `tre}ehz` uk` kezljlalbc` i`mzyea t`r` ` lozehml jl}

    t`rkezrl} e jl} e}t`ml} je e}z`jl}(

    L trloaek` j` e}zck`ml jl} e}t`ml} je e}z`jl}! }er jcycjcjl ek zre} ez`t`}7Icazr`bek! ]u`ycw`ml e Treyc}l( @ trltl}z` ` }ebucr }utle mlhnemcjl l yezlr je

    t`rkezrl} ! l pue hl lmlrre h` trzcm`! }ehjl heme}}rcl e}zck+al z`koek( C}zl

    }er ieczl uzcacw`hjl l} `ablrczkl} jl m`tzual =! Kezrltlac}+N`}zchb} e @klzr`jlr

    je Bcoo}(

    Icazr`bek

    @ ez`t` je ffazr`bek i`w+}e `zr`ye} j`} epu`mle} jl }c}zek`! pue }l retre}ehz`j`} `

    t`rzcr j`} jc}zrcoucmle} je trlo`ocacj`je ` trclrc t.zqJz0#! ` jc}zrcoucml trejczcy`uk t`}}l ` irehze! t.szqJz0# e ` jc}zrcoucml tl}zerclrc je t.zqJz#! ek pu`apuerzektl z 0! lhje Jz e ` retre}ehz`ml t`r` zlj` ` chilrk`ml e~c}zehze `ze lch}z`hze z(

    Jc}zrcoucml Trclrc ek z7

    t.zqJz0! # ;

    t.zqz0! Jz0! #t.z0qJz0! #jz0

    0>

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    37/118

    Jc}zrcoucml Trejczcy` uk t`}}l7

    t.szqJz0! # ;

    t.szqz! Jz0! #t.zqJz0! #j

    Jc}zrcoucml Tl}zerclrc7

    t.zqJz! # ; t.szqz! Jz0! #t.zqJz0! #t.szqJz0! #

    ]u`ycw`ml

    Kejc`hze t.ZqJZ! #! re}uaz`hze j` Icazr`bek! ` jeh}cj`je mlhguhz }u`ycw`j`t.07ZqJZ#! e lozcj` je ilrk` remur}cy uzcacw`hjl ` aec kuazctacm zcy` j`} trlo`+

    ocacj`je}( @ hlz`ml e}z`oeaemcj` e ke}k` uzcacw`j` tlr Fcz`b`` .03>2#! lhje

    07Z! retre}ehz` l} e}t`ml} je e}z`jl} hl ch}z`hze 0 `l Z+e}ckl ch}z`hze(

    t.07ZqJZ! # ; t.ZqJZ! #t.07Z0qZ! JZ! #; t.ZqJZ! #t.Z0qZ! JZ! #t.07Z?qZ! Z0! JZ! #;

    (((

    ; t.ZqJZ! #Z0

    z;0 t.zqz&0! JZ! # .=(=#L zerkl jehzrl jl trljuzlrcl tlje }er lozcjl j` }ebuchze ilrk`7

    t.zqz&0! JZ! # ; t.zqz&0! Jz! sz&07Z! #;

    t.sz&07Zqz! z&0! Jz! #t.zqz&0! Jz! #t.sz&07Zqz&0! Jz! #

    lhje z e chjetehjehze je pu`apuer lo}ery`ml iuzur`! mlhjcmclh`jl d z&0! Jz e (

    Albl7

    t.zqz&0! JZ! # ; t.sz&0!Zqz&0! Jz! #t.zqz&0! Jz! #t.sz&07Zqz&0! Jz! #

    ; t.zqz&0! Jz! # .=(:#

    ]uo}zczuchjl ` epu`ml .=(:# ek .=(=#! jezerkch`+}e ` jeh}cj`je mlhguhz

    }u`ycw`j` t.ZqsZ! # j`j` tlr7

    t.07ZqJZ! # ; t.ZqJZ! #Z0z;0

    t.zqz&0! Jz! #

    03

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    38/118

    Treyc}`l

    @ jeh}cj`je trejczcy` t`r` F t`}}l} ` irehze tlje }er lozcj` t`r` m`j` ch}z`hze

    je zektl z! mlhjcmclh`j` ` chilrk`ml jc}tlhyea h`pueae ke}kl ch}z`hze( E}z`

    `y`ac`ml e re`acw`j` je ilrk` czer`zcy`! ` t`rzcr jl kljeal .=(0#! e tlje }er yercff+

    m`j` ` }ebucr( ]utlhn` pue7

    t.z&0qz! Jz! # ; t.z&0qz! #

    lu }eg ! ` jc}zrcoucml tl}zerclrc t.z&0qz! Jz! #! e chjetehjehze j` chilrk`mljc}tlhyea `ze l ch}z`hze z(

    @ jeh}cj`je trejczcy` 0 t`}}l ` irehze e j`j` tlr7

    t.z&0qJz! # ;

    t.z&0qz#t.zqJz! #jz

    Beher`acw`hjl! ` jeh}cj`je trejczcy` t.z&fqJz! # t`r` F t`}}l} ` irehze e j`j`tea` remur}l7

    t.z&fqJz! #

    t.z&fqz&f0#t.z&f0qJz! #jz&f0

    t`r` f;0!(((!F(@ jeh}cj`je j` pu`hzcj`je Sz! ` }er treyc}z`! tlje }er jezerkch`j` tlr7

    t.sz&FqJz! # ;

    t.sz&Fqz&F#t.z&FqJz! #jz&F .=(5#

    =(5(0 Kljeal Ache`r Jchkcml Hlrk`a

    @ze e}ze klkehzl i`alu+}e je ilrk` ber`a ` re}teczl jl} kljeal} jchkcml}! `blr`

    }er chzrljuwcjl l kljeal jchkcml ek }u` ilrk` k`c} uzcacw`j`( T`r` m`j` ch}z`hzeje zektl z! ` e}zruzur` ache`r jchkcm` tlje }er jeffhcj` mlkl7

    Sz ; Izz & z! z H.4! Yz# .=(9#

    z ; Bzz0 & z! z H.4! Rz# .=(2#

    lhje7

    Sz

    yezlr je lo}ery`mle} r

    06

    z yezlr je t`rkezrl} h 06

    ?4

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    39/118

    Iz k`zrcw mlhnemcj` h r6

    Bz k`zrcw mlhnemcj` h h6

    Yz k`zrcw mly`rchmc` mlhnemcj` r r6 Rz k`zrcw mly`rchmc` mlhnemcj` h h6

    z e z }l chjetehjehze} ehzre }c(

    L m`tzual 5! i`r ` uzcacw`ml je kljeal} jchkcml} t`r` ` yla`zcacj`je je uk

    `zcyl ffh`hmecrl! e remeoek ` hlkehma`zur` je Kljeal} je Yla`zcacj`je E}zlm}zcm`(

    @} k`zrcwe} Iz! Bz! Yz e Bz! }l mlh}cjer`j`} mlhnemcj`} t`r` m`j` ch}z`hze je

    zektl z! e tljek jetehjer je uk yezlr je t`rkezrl} ( L ehilpue o`se}c`hl t`r`e}z` ma`}}e je kljeal} jchkcml} tlje }er ehmlhzr`jl ek Re}z e N`rrc}lh .0332# e

    ek Kcblh e B`kerk`h .0333#( @ `olrj`bek jl tlhzl je yc}z` ma}}cm` tlje }er

    yc}zl ek Klrezch e Zlalc .?449#( He}z` jc}}erz`ml ` `olrj`bek }er j`j` `teh`}

    `zr`ye} jl mlhze~zl o`se}c`hl(

    Icazrl je F`ak`h

    L Icazrl je F`ak`h e uk` `olrj`bek e}temffm` t`r` `y`ac`r ` jc}zrcoucml ` tl}+

    zerclrc t.zqJz! # o`}e`jl h` jc}zrcoucml trclrc t.zqJz0! #( L Icazrl je F`ak`he uk `ablrczkl pue terkcze `zu`acw`r je ilrk` remur}cy` ` jc}zrcoucml jl} e}t`ml}

    je e}z`jl} z! ` t`rzcr j` jc}tlhcocacj`je je uk` hly` lo}ery`ml( @} ez`t`} je

    trlme}}l je ffazr`bek }erl `tre}ehz`j`} ` }ebucr! lhje `} jc}zrcoucmle} trclrc! tl}+

    zerclrc e trejczcy`! `tre}ehz`k jc}zrcoucml hlrk`a( E}ze re}uaz`jl e}z trly`jl ek

    Re}z e N`rrc}lh .0332#(

    Jc}zrcoucml Trclrc zqJz0! 7

    t.zqJz0! # H.`z! _z# .=(>#lhje7 `z ; Bzkz0

    _z ; BzMz0Bz & Rz

    ?0

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    40/118

    Jc}zrcoucml Trejczcy` 0 t`}}l szqJz0! 7

    t.szqJz0! # H.iz! Pz# .=(3#lhje7 iz ; I

    z `z

    Pz ; Iz_zIz & Yz

    Jc}zrcoucml Tl}zerclrc zqJz! 7

    t.zqJz! # H.kz! Mz# .=(04#lhje7 @z ; _z

    IzPz

    b`hnl je F`ak`h

    kz ; `z & @z.sz

    iz#

    Mz ; _z @zPz@z

    ]u`ycw`jlr je F`ak`h

    L ]u`ycw`jlr je F`ak`h e l `ablrczkl uzcacw`jl t`r` jezerkch`r ` jc}zrcoucml

    }u`ycw`j` je t.zqJZ! #! t`r` z ; 0!(((!Z( L `ablrczkl chcmc`+}e hl ch}z`hze Zlozcjl ` t`rzcr jl Icazrl je F`ak`h e termlrre zlj`} `} lo}ery`mle} je ilrk` re+

    mur}cy`( Jezerkch`r ` jc}zrcoucml }u`ycw`j` e uzca pu`hjl ` chilrk`ml jc}tlhyeay`c `aek jl ch}z`hze z( Hlze pue! pu`hjl uzcacw`+}e uk }c}zek` ek zektl re`a! `

    jc}zrcoucml tl}zerclrc ilrhemcj` tea` ffazr`bek e ` keanlr chilrk`ml jc}tlhyea( @

    chilrk`ml lozcj` teal ]u`ycw`jlr je F`ak`h hl zek uzcacj`je t`r` re`acw`ml

    je treyc}le}! k`} e o`}z`hze y`hz`gl}l pu`hjl }e zr`z` je `hac}e} rezrl}temzcy`}!

    zehjl mlkl logezcyl uk keanlr mlhzrlae jl }c}zek`(

    Jeffhchjl7 Oz ; MzBz&0_0z

    t.zqJZ! # H.kz! Mz# .=(00#lhje7 kz ; kz & Oz.kz&0 `z&0#

    Mz ; Mz & Oz.Mz&0 _z&0#Oz

    @ remur}l e chcmc`acw`j` mlk kZ ; kZ e MZ ; MZ( @ trly t`r` l `ablrczkl

    ]u`ycw`jlr je F`ak`h e re`acw`j` uzcacw`hjl l trchmtcl j` chjuml reyer}` e tlje

    }er yc}z` ek Re}z e N`rrc}lh .0332#(

    ??

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    41/118

    M`tzual :

    Kljeal} mlk Yla`zcacj`je

    Chy`rc`hze hl Zektl

    He}ze m`tzual }erl `tre}ehz`jl} zre} kljeal} t`r` tremcffm`ml je ltmle}! i`wehjl

    u}l j` epu`ml je O] chzrljuwcj` hl m`tzual ?( L} kljeal} i`wek u}l j` nctlze}e

    je yla`zcacj`je chy`rc`hze `l alhbl jl zektl! }u`} jcierehm`} trlyek j` chilrk`ml

    uzcacw`j` t`r` e}zck`r e}z` yla zcacj`je( L m`tzual e}z jcycjcjl ek ju`} }emle}!

    lhje ` trckecr`! :(0! zr`z` jl kljeal pue i`w u}l j` chilrk`ml mlhzcj` ek nc}zlrcml}

    je rezlrhl}( @ }eml }ebuchze! :(?! chzrljuw l} jlc} kljeal} re}z`hze}! pue chmlrtl+

    r`k d chilrk`ml je nc}zlrcml} je treml} je ltmle}! h` jezerkch`ml j` yla`zcacj`je(

    L logezcyl j` chmau}l jl} treml} nc}zlrcml} je ltmle}! yc}` `ukehz`r ` tremc}l h`

    jc}zrcoucml ` tl}zerclrc j` yla`zcacj`je( L kljeal j` }eml :(0 zek ilrze chuehmc`

    jl zr`o`anl je Br`s .?44?#! ehpu`hzl l} kljeal} j` }eml :(?! jl zr`o`anl Tla}lh

    e Gln`hhe} .?449#(

    :(0 Yla`zcacj`je Chy`rc`hze mlk Chilrk`ml jl

    _ezlrhl + Kljeal `

    Sz ; &

    zz! z H.4! 0# .:(0#

    E}ze kljeal e uk` retre}ehz`ml t`r` epu`ml ber`jlr` je treml} je uk `zcyl!

    epu`ml .?(0=#! chzrljuwcj` hl m`tzual ?( Lhje Sz ; ah.]z&0,]z# H.! ?z#

    ?=

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    42/118

    e l rezlrhl hl ch}z`hze z e ; . ?,?#z e l y`alr e}ter`jl j` jcierehm` jl}alb`rczkl} jl} treml} .alb+rezlrhl}#! pue ilc ret`r`kezrcw`jl t`r` }cktacffm`r l}

    mamual}( He}ze kljeal ` uhcm` chilrk`ml uzcacw`j` t`r` e}zck`r ` yla`zcacj`je e

    trlyehcehze jl nc}zlrcml jl} rezlrhl}(@ jc}zrcoucml ` tl}zerclrc mlhguhz` je e ?! .:(?#! e m`amua`j` ` t`rzcr jl yezlr

    je rezlrhl} SZ ; .s0!(((!sZ# lo}ery`jl}! e `} jc}zrcoucmle} ` trclrc trltl}z`} zek

    jc}zrcoucml Hlrk`a q? H.k ! R?# e B`k`+Chyere}` ? BC.`! o#(

    t.! ?qSZ# ;Zz;0

    t.szq! ?#t.q?#t.?# .:(?#

    L `ablrczkl u}`jl t`r` e}zck`r l} t`rkezrl} e l @kl}zr`jlr je Bcoo}(

    Ekolr` e~c}z` uk` }lauml `h`azcm` t`r` `} jc}zrcoucmle} jl} t`rkezrl} .Kcblh

    e B`kerk`h ! 0333#! crekl} `tacm`r zemhcm`} mlktuz`mclh`c}! mlkl }ckua`ml

    e}zlm}zcm`! m`}l }eg` e~cbcjl l ke}kl t`r` l} jek`c} kljeal} je}z` jc}}erz`ml(

    @} jc}zrcoucmle} mlhjcmclh`c} mlktaez`} jl} t`rkezrl} e 7

    q? HsR & kz

    R & z!

    ?zR

    R & z .:(=#?q BC

    Z

    ?& 0 & `!

    R.P & Z. s#?# & z. k#? & ?Rzo?zR

    .:(:#

    lhje7 P ;Zz;0

    .sz #? e s ; 0Z

    Zz;0

    sz

    ]ckua`ml

    @ `y ac`ml jl `ablrczkl ilc re`acw`j` ` t`rzcr je uk mlhguhzl je j`jl} ber`+

    jl} `rzcffmc`akehze uzcacw`hjl ` epu`ml .?(0=#! mlk l} t`rkezrl} ; 4(9> e

    ? ; 4(??! ehmlhzr`jl} hl kerm`jl ffh`hmecrl or`}caecrl( Ilr`k }ckua`j`} 094

    y`alre}! lhje l} =4 ffh`c} ilr`k uzcacw`jl} mlkl `kl}zr` ze}ze e l} jek`c} u}`jl}

    mlkl `kl}zr` zrechl ]Z ; .}0!(((!}Z# + `kl}zr` zrechl! lhje Z;0=4#( L mehrcl je

    }ckua`ml ilc ?5? jc`} uzec} je uk `hl! cktacm`hjl ek z ; 0,?5?(

    @ t`rzcr j` `kl}zr` ze}ze jl `zcyl .}Z&0!(((!}Z&=4#! ilc }ckua`jl uk mlhguhzl mlk

    =4 treml} .lZ&0!(((!lZ&=4#! uzcacw`jl} h` yercffm`ml j` tremcffm`ml( @ ber`ml jl}

    treml} j` ltml ilc re`acw`j` uzcacw`hjl ` e}zruzur` O] & z! lhje z H.4! ?O]#!

    ?:

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    43/118

    mlk ?O] ; 4(=( L} t rkezrl} t`r` l kljeal O] }l7 treml je e~ermmcl F ;

    _*54! 44! yla`zcacj`je ? ; 4(??! z`~` je gurl} acyre je rc}ml r ; 00(?5 e j jc`} t`r`

    l yehmckehzl! lhje j ; =4!(((! 0(

    Icbur` :(07 Treml} ]Z ; .}z!(((!}Z# }ckua`jl} uzcacw`hjl ` epu`ml ?(0= e l}

    t`rkezrl}7 ; 4(9> e ? ; 4(??(

    0=4 jc`}

    ]z

    4 ?4 :4 94 >4 044 0?4

    =5

    :4

    :5

    54

    Icbur` :(?7 _ezlrhl} SZ ; .sz!(((!sZ# t`r` l `zcyl }ckua`jl(

    0=4 jc`}

    Sz

    4 ?4 :4 94 >4 044 0?4

    4(4

    5

    4(4

    5

    L `ablrczkl @kl}zr`jlr je Bcoo} jezerkch` ` jc}zrcoucml ` tl}zerclrc je

    e ?! pue }l l} t`rkezrl} jl kljeal .:(0#( Uzcacw`hjl ` zr`h}ilrk`ml

    ; ,z & ?,?! jezerkch`+}e ` jc}zrcoucml ` tl}zerclrc je (

    L `ablrczkl7

    0( Chcmc acwe .4#! ?.4# e ?.4#6

    ?( T`r` c 0! `kl}zre je .c# e ?.c#! je .:(=# e .:(:#! re}temzcy`kehze 6

    =( M`amuae7

    .c# ; .c#,z & ?.c#,?6

    ?5

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    44/118

    treyc}l7 .}Z&0!(((!}Z&=4#

    .c#! uzcacw`hjl ` epu`ml .?(0=#6

    tremcffm`ml 07 .O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4##.c#! ` t`rzcr

    je .?(0=#6

    tremcffm`ml ?7 .O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4##.c#! ` t`rzcr

    je .?(0=# e .}Z&0!(((!}Z&=4#

    .c#6

    :( I`m` c;c&0 e ylaze t`r` ?! retcz` `ze mlhyerbcr(

    @ tremcffm`ml 0 uzcacw` l mlhguhzl je y`alre} }ckua`jl} t`r` ` `kl}zr` ze}ze! lu

    }eg`! y`alre} treyc`kehze mlhnemcjl}! .}Z&0!(((!}Z&=4#( @ tremcffm`ml ? uzcacw` l

    mlhguhzl je =4 treyc}le} t`r` l `zcyl .}Z&0!(((!}Z&=4#! re`acw`j`} hl zek =! l}

    jek`c} t`rkezrl} jl kljeal O] }l l} ke}kl} u}`jl} h` }ckua`ml j`} ltmle}(

    L} nctert`rkezrl} j`} jc}zrcoucmle} ` trclrc }l7 k ; 4! R ; 04=! ` ; 4(4444440

    e o ; 4(4444440(

    Icbur` :(=7 Nc}zlbr`k`} e m`jec` t`r` `kl}zr` j` jc}zrcoucmle} ` tl}zerclrc je e

    ? + kljeal `(

    Ilr`k ber`j`} 09(444 czer`mle}! e `} >(444 czer`mle} chcmc`c} ilr`k je}m`rz`j`}

    mlkl `puemckehzl j` m`jec`( @ Icbur` :(= `tre}ehz` l} nc}zlbr`k`} e `} m`jec`}t`r` `} jc}zrcoucmle} ` tl}zerclrc je e ?! re}temzcy`kehze( L y`alr yerj`jecrl jl

    ?9

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    45/118

    t`rkezrl hl nc}zlbr`k`! e}z retre}ehz`jl tea` achn` jeh}` yerje e h` m`jec` tea`

    yerkean`( L} re}uaz`jl} re}ukcjl} j`} jc}zrcoucmle} ` tl}zerclrc e}zl h` z`oea` :(0

    ` }ebucr7

    Z`oea` :(07 _e}ukl j`} Jc}zrcoucmle} Tl}zerclrc} je e ? + kljeal `

    Y`alr _e`a Kejc` Je}ycl T`jrl ?(5% 32(5%

    4(9> 4(992= 4(::9? 4(?0=9 0(5=??? 4(?? 4(?43> 4(40>5 4(029: 4(?:30

    T`r` jezerkch`r l treml `zr`ye} j` epu`ml O]! hl e heme}}rcl ` y`alr je (

    @ ffbur` :(: kl}zr` l} re}uaz`jl} j` jc}zrcoucml trejczcy t.}Z&0!(((!}Z&=4#! t`}}l

    = jl `ablrczkl( @ treyc}l .achn` yerje jeh}`# ilc m`amua`j` ` t`rzcr jl} y`alre}

    kejcl} j jc}zrcoucml e l} chzery`al} mlk 35% je mrejcocacj`je .achn`} yerkean`}

    zr`meg`j`}#! ` t`rzcr jl} pu`hzc} p4(4?5 e p4(325( @ achn` e}mur jeh}`! retre}ehz` l}

    y`alre} }ckua`jl} mlkl `kl}zr` ze}ze t`r` l `zcyl(

    Icbur` :(:7 @zcyl }ckua`jl t`r` `kl}zr` ze}ze! treyc}l e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal `(

    =4 Jc`}

    ]z

    4 5 04 05 ?4 ?5 =4

    :4

    94

    >4

    _e`a Treyc}zl CM 35%

    @ ffbur` :(5 `tre}ehz` l} re}uaz`jl} j` tremcffm`ml lozcjl} tea` jc}zrcoucml

    `kl}zr`a

    t

    O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4#

    ! ber`j` teal t }}l = jl `a+

    blrczkl( E}ze} re}uaz`jl} uzcacw`k l} y`alre} }ckua`jl} t`r` `kl}zr` ze}ze jl

    `zcyl }Z&0!(((!}Z&=4! lu }eg`! l treml j` ltml e m`amua`jl mlk l y`alr jl `zcyl

    treyc`kehze mlhnemcjl( L y`alr je O] .achn` yerje# ilc m`amua jl ` t`rzcr j`}

    kejc`} e l} chzery al} mlk 35% je mrejcocacj`je .achn`} yerkean`} zr`meg`j`}#!

    ?2

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    46/118

    ` t`rzcr jl} pu`hzc} p4(4?5 e p4(325( @ achn` e}mur` jeh}` }l l} treml} j` ltml

    .lZ&0!((((!lZ&=4#! }ckua`jl} mlkl `kl}zr` ze}ze t`r` ` ltml(

    Icbur` :(57 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al} mlk

    35% je mrejcocacj`je! uzcacw`hjl l `zcyl }ckua`jl t`r` ` `kl}zr` ze}ze + kljeal `(

    =4 Jc`}

    Lz

    4 5 04 05 ?4 ?5 =4

    ?

    9

    04

    _e`a Treyc}zl CM 35%

    L} re}uaz`jl} j` jc}zrcoucml `kl}zr`a t.O].}Z&0! ?! j ;

    =4#!(((!O].}Z&=4! ?! j ; 4##! t }}l = jl `ablrczkl! e}zl `tre}ehz`jl} h`

    ffbur` :(9( @ tremcffm`ml uzcacw` l} y`alre} pue ilr`k treyc}zl} t`r` l `zcyl jur`hze

    l t`}}l = jl `ablrczkl( L y`alr je O] .achn` yerje# ilr`k m`amua`jl} ` t`rzcr j`}

    kejc`} e l} chzery`al} mlk 35% je mrejcocacj`je .achn`} yerkean`} zr`meg`j`}#! `

    t`rzcr jl} pu`hzc} p4(4?5 e p4(325( @ achn` e}mur` jeh}` }l l} treml} }ckua`jl} j`

    ltml .lZ&0!((((!lZ&=4# }ckua`jl}(

    Icbur` :(97 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl treyc}zl + kljeal `(

    =4 Jc`}

    Lz

    4 5 04 05 ?4 ?5 =4

    4

    04

    ?4 _e`a Treyc}zl CM 35%

    @l mlkt`r`r `} ffbur`} :(5 e :(9 termeoe+}e pue ` trckecr` `tre}ehz` uk` jc}+

    zrcoucml t`r` l} treml} O] k`c} tremc}l}! tlr uzcacw`r l y`alr mlhnemcjl0 t`r` l

    0L} y`alre} mlhnemcjl} }l l} ke}kl} pue l} y`alre} }ckua`jl}(

    ?>

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    47/118

    `zcyl( E}ze} re}uaz`jl} yeek mlktrly`r pue l y`alr jl `zcyl mlhzek br`hje t`rze

    j chilrk`ml re`a jl treml j` ltml(

    :(? Yla`zcacj`je Chy`rc`hze mlk Chilrk`ml jl}

    _ezlrhl} e je Ltmle}

    He}z` }eml }erl `tre}ehz`jl} jlc} kljeal}( L trckecrl uzcacw` ` chilrk`ml jl

    `zcyl ek mlhguhzl mlk ` chilrk`ml je uk` ltml je mlktr`( L }ebuhjl e uk`

    eylauml jl trckecrl! e uzcacw` ` chilrk`mle} mlhzcj`} hl `zcyl e ek ju`} ltmle}

    je mlktr` jcierehze}( L} kljeal} zek mlkl logezcyl jezerkch`r ` jc}zrcoucml j`

    yla`zcacj`je ? e tremcffm`r ltmle}(

    Tla}lh e Gln`hhe} .?449# jeffhcr`k mlkl ]chbua`rcj`je E}zlm`}zcm`! ` rea`ml

    jcrez` ehzre ` yla`zcacj`je e l treml je uk` ltml m`amua`j` `zr`ye} kljeal je

    O]( T`r` eae} e}z` rea`ml jcrez` jeyerc` }er je}iecz`! g pue hl }e yercffm`y ek

    trloaek`} re`c} je tremcffm`ml( @ }lauml trltl}z` ilc ` chmau}l je uk` epu`ml

    `l kljeal .:(0#! pue retre}ehz`}}e ` chilrk`ml mlhzcj` hl treml je uk` ltml(

    :(?(0 Yla`zcacj`je Chy rc`hze mlk Chilrk`ml jl _ezlrhl e

    je Uk` Ltml + Kljeal o

    Sz ; &

    zz .:(5#

    Lz ; O].?! Sz# & z z! z H.4! 0# .:(9#

    @ trckecr` epu`ml e ` ret`r`kezrcw`ml je .?(0=#! lhje Sz ; ah.]z&0,]z# e l

    rezlrhl hl ch}z`hze z e ; . ?,?#z e l y`alr e}ter`jl t`r` l} alb+rezlrhl}(@ epu`ml .:(9# chzrljuw ` chilrk`ml jl treml je uk` ltml hl ch}z`hze z( L

    rezlrhl e ` ltml hl ch}z`hze z zek jc}zrcoucml hlrk`a7 Sz H.! z?# e Lz H

    O].Sz! ?#! ?

    ! re}temzcy`kehze(

    E}ze kljeal zek uk t`rkezrl ` k`c} t`r` e}zck`r! ?! chzer+

    trez`jl mlkl ` chmerzew` je kerm`jl( T`r` }cktacffm`r ` hlz`ml

    jeffhc+}e ; .! ?! ?#( @ jc}zrcoucml ` tl}zerclrc mlhguhz`

    ?3

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    48/118

    t.qSZ! LZ#! lhje SZ ; .s0!(((!sZ# e LZ ; .l0!(((!lZ#! e lozcj`tlr .:(2# e `} jc}zrcoucmle} ` trclrc trltl}z } }l7 H.k! ?#!? BC.`! o# e ? BC.m! j#(

    t.qSZ! LZ# ;Zz;0

    t.lzqsz! #t.szq! ?#t.q?#t.?#t.?# .:(2#

    L} `ablrczkl} uzcacw`jl} t`r` jezerkch`r `} jc}zrcoucmle} ` tl}zerclrc} }l

    @kl}zr jlr je Bcoo} e Kezrltlac}+N`}zchb}( @kol} }l uzcacw`jl}! tlc} ` jc}+

    zrcoucml mlhjcmclh`a mlktaez`! t`r` ` yla`zcacj`je ?! hl `tre}ehz` uk` ilrk`

    mlhnemcj`(

    @} jc}zrcoucmle} mlhjcmclh`c} mlktaez`} je ! ? e ?7

    q? H

    RsZ & kzZ R & z

    !R ?z

    Z R & z

    .:(>#

    ?q? BC

    Z & ?m

    ?!

    0

    ?

    Zz;0

    lz O].sz! ?#

    ?& ?j

    .:(3#

    t.?q! ?# .?#.Z&0&?`

    ? &0# e~t

    P0

    ??Rz

    e~t

    P?

    ??

    .:(04#

    lhje7 P0 ; RZz;0

    .sz #? & z. k#? & ?oRz e P? ;Zz;0

    lz O].sz! ?#

    ?

    @ jc}zrcoucml trltl}z` uzcacw`j` hl `ablrczkl Kezrltlac}+N`}zchb} e t`rze jl

    humael j` jc}zrcoucml mlhjcmclh`a mlktaez` t.?q! ?#( @ t`rze e}mlancj` zekjc}zrcoucml B`k` Chyer}`! uk` jc}zrcoucml mlhnemcj` e imca je }e `kl}zr`r(

    ?q BC

    Z & 0 & ?`

    ?!

    P0?Rz

    .:(00#

    lhje7 P0 ; RZz;0

    .sz #? & z.k#? & ?oRz

    @ chilrk`ml ilrhemcj` hl treml j` ltml e chmlrtlr`j` `l kljeal hl ze}ze je

    `mecz`ml jl `ablrczkl Kezrltlac}+N`}zchb}!

    =4

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    49/118

    T.?.c#! ?.c&0## ; kch0!e~t

    0

    ??.c#

    Zz;0

    lz O].sz! ?.c&0##

    ?

    e~t 0

    ??.c#

    Zz;0

    lz O].sz! ?.c##?

    .:(0?#

    ]ckua`ml

    L `ablrczkl e `y ac`jl ` t`rzcr je j`jl} }ckua`jl} `rzcffmc akehze( L} treml} jl

    `zcyl ilr`k }ckua`jl} h` }eml `hzerclr( _eaekor`hjl pue l trlme}}l uzcacwlu `

    epu`ml .?(0=#! mlk t`rkezrl} ; 4(9> e ?

    ; 4(??( L} j`jl} ber`jl} ilr`kjcycjcjl} mlhilrke ieczl `hzerclrkehze! l} uazckl} =4 y`alre} ilr`k uzcacw`jl} t`r`

    `kl}zr` ze}ze e l} 0=4 re}z`hze} uzcacw`jl} mlkl `kl}zr` zrechl! l} y`alre} reierehze}

    ` `kl}zr` zrechl tljek }er yc}zl} h` ffbur` :(0 j` }eml `hzerclr(

    He}z` }eml }e i`w heme}}rcl ber`r y`alre} t`r` uk` ltml! pue }er uzcacw`j`

    }ckuaz`he`kehze mlk l} rezlrhl}? t`r` ` e}zck`r l} t`rkezrl}( Ilr`k ber`jl} y`+

    alre} t`r` l} treml} je uk` ltml je mlktr`! jl }eu a`hm`kehzl `l }eu yehmckehzl(

    L} 0=4 treml} t`r` l `zcyl j` `kl}zr` zrechl ilr`k uzcacw`jl}! e l} treml} j ltml

    ilr`k }ckua`jl} ` t`rzcr j` epu`ml .:(9#( L} t`rkezrl} uzcacw`jl} ilr`k! treml

    je e~ermmcl _*:5! 44! yla`zcacj`je ? ; 4(??! z`~` je gurl} acyre je rc}ml r ; 00! ?5%

    e .Z+z# jc`} t`r` l yehmckehzl! mlk Z;0=4( L zerkl je chmerzew` j` epu`ml .:(9#

    ilc ff~`jl ek ? ; 4(?(

    T`r` `y`ac`r ` tremcffm`ml re`acw`j` teal kljeal o ilc uzcacw`j` ` ltml ber`j`

    mlkl `kl}zr` ze}ze h` }eml :(0( Jcierehzekehze j` ltml }ckua`j` he}z` }eml! `

    ltml ber`j` mlkl `kl}zr` ze}ze hl mlhzrcouc t`r` ` e}zck`ml jl} t`rkezrl}!

    }u` uhcm` iuhml e yercffm`r ` tremcffm`ml re acw`j` teal `ablrczkl( L trlme}}l

    e}z` je}mrczl hl zltcml }ckua`ml! j` }eml `hzerclr d e}z`( Aekor`hjl pue l}

    t`rkezrl} u}`jl}! treml je e~ermmcl F ; _*54! 44! yla`zcacj`je ? ; 4(??! z`~`

    acyre je rc}ml r ; 00(?5% e zektl `ze l yehmckehzl je =4 jc`}( @ epu`ml .:(=# e `

    ke}k` uzcacw`j` t`r` }ckua`r ` ltml j` `kl}zr` ze}ze j` }eml :(0(

    ?E mlkuk }e reiercr `l} treml} jl `zcyl e `l} rezlrhl} mlkl }ehjl ` ke}k` chilrk`ml! yc}zl

    pue `kol} }l lozcjl} i`mcakehze uk ` t`rzcr jl luzrl(

    =0

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    50/118

    Icbur` :(27 Ltml ber`j` t`r` `kl}zr` ze}ze LZ ; .l0!(((!lZ#! mlk Z;0=4(

    4 ?4 :4 94 >4 044 0?4

    4

    ?

    :

    9

    >

    0=4 Jc`}

    Lz

    L `ablrczkl7

    0( Chcmc acwe .4#! ?.4# e ?.4#6

    ?( T`r` c 0! `kl}zre .c# e ?.c# ! ` t`rzcr je .:(># e .:(3#! re}temzcy`kehze 6

    =( @kl}zre ?.c&0#! ` t`rzcr je .:(00#6

    :( Bere u U.4! 0#! ]e u 1 T.?.c#! ?.c&0##! lhje T.# e lozcjl ek .:(0?#!?.c&0# ?.c&0#! m`}l mlhzrrcl ?.c&0# ?.c# 6

    5( M`amuae7

    .c# ; .c#,z & ?.c#,?6

    Treyc}l7 .}Z&0!(((!}Z&=4#

    .c#! ` t`rzcr je .?(0=#6

    Tremcffm`ml 07 .O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4##.c#! ` t`rzcr

    je .?(?0#6

    Tremcffm`ml ?7 .O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4##.c# ` t`rzcr

    je .?(?0# e .}Z&0!(((!}Z&=4#.c#6

    9( I`m` c;c&0 e ylaze t`r` ?! retcz` `ze mlhyerbcr6

    @ tremcffm`ml 0 uzcacw` l mlhguhzl je y`alre} }ckua`jl} t`r` ` `kl}zr` ze}ze!

    lu }eg`! y`alre} treyc`kehze mlhnemcjl}! .}Z&0!(((!}Z&=4#( @ tremcffm`ml ? uzcacw`

    l mlhguhzl je =4 treyc}le} t`r` l `zcyl .}Z&0!(((!}Z&=4#! re`acw`j`} hl zek 5( L}

    jek`c} t`rkezrl} jl kljeal O] }l l} ke}kl} u}`jl} h` }ckua`ml j`} ltmle}(

    L} nctert`rkezrl} j`} jc}zrcoucmle} ` trclrc }l7 k ; 4! R ; 04=! ` ; 4(4444440!

    o ; 4(4444440! m ; 4(4444440 e j ; 4(4444440(

    =?

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    51/118

    Icbur` :(>7 Nc}zlbr k`} e m`jec` t`r` `kl}zr` j` jc}zrcoucmle} ` tl}zerclrc je !

    ? e ?+ kljeal o(

    Ilr`k ber`j`} 09(444 czer`mle}! e `} >(444 czer`mle} chcmc`c} ilr`k je}m`rz`j`}

    mlkl `puemckehzl j` m`jec`( @ Icbur` :(> `tre}ehz` l} nc}zlbr`k`} e `} m`jec`}

    t`r` `} jc}zrcoucmle} ` tl}zerclrc je ! ? e ? re}temzcy`kehze( L y`alr yerj`jecrl

    jl t`rkezrl hl nc}zlbr`k` e}z retre}ehz`jl tea` achn` jeh}` yerje e h` m`jec`

    tea` yerkean`( L} re}uaz`jl} re}ukcjl} j`} jc}zrcoucmle} ` tl}zerclrc e}zl h` z`oea`

    :(?(

    Z`oea` :(?7 _e}ukl j`} Jc}rcoucmle} jl} t`rkezrl} ! ? e ? + kljeal o(

    Y`alr _e`a Kejc` Je}ycl T`jrl ?(5% 32(5%

    4(9> 4(>>4: 4(5::3 4(0>>5 0(3554? 4(?4 4(???9 4(4??2 4(0>?= 4(?20:

    ? 4(?? 4(?=44 4(4499 4(?020 4(?:?5

    L} re}uaz`jl} t`r` ` jc}zrcoucml jl t`rkezrl }l kuczl t`remcjl} mlk l}

    ==

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    52/118

    lozcjl} h` }eml `hzerclr :(0( Tlrek! l t`rkezrl je chzere}}e ? `tre}ehzlu uk

    `ukehzl je tremc}l }cbhcffm`zcyl( L jeycl t`jrl j` }u` jc}zrcoucml ` tl}zerclrc

    rejuwcu je 4(40>5 t`r` 4(4499! mlhffrk`hjl l b`hnl eiezcyl `l }e lo}ery`r treml}

    je uk` ltml ek mlhguhzl mlk l} rezlrhl}! `l }e e}zck`r ` yla`zcacj`je(L `ukehzl j` tremc}l je ? chuehmclu ` jc}zrcoucml trejczcy` jl `zcyl

    t.}Z&0!(((!}Z&=4#! pue z`koek `tre}ehzlu uk b`hnl je tremc}l( @ ffbur` :(3 cau}+

    zr` l} re}uaz`jl} lozcjl} hl t`}}l 5 jl `ablrczkl( @ treyc}l .achn` yerje jeh}`# e

    m`amua`j` ` t`rzcr jl} y`alre} kejcl} j` jc}zrcoucml trejczcy` e l} chzery`al} mlk

    35% je mrejcocacj`je .achn`} yerkean`} zr`meg`j`}#! m`amua`j`} ` t`rzcr jl} pu`hzc}

    p4(4?5 e p4(325( @ achn` e}mur` jeh}` }l l} y`alre} }ckua`jl} mlkl `kl}zr` ze}ze jl

    `zcyl h` }eml :(0(

    Icbur` :(37 @zcyl }ckua`jl t`r` `kl}zr` ze}ze! treyc}l e chzery`al} mlk 35% je

    mrejcocacj`je + kljeal o(

    =4 Jc`}

    ]z

    4 5 04 05 ?4 ?5 =4

    :4

    94

    >4

    _e`a Treyc}zl CM 35%

    @ ffbur` :(04 `tre}ehz` l} re}uaz`jl} j` tremcffm`ml lozcjl} tea` jc}zrcoucml

    `kl}zr`a

    t

    O].}Z&0!

    ?

    ! j ; =4#!(((!O].}Z&=4!

    ?

    ! j ; 4#

    t`r` l kljeal o! t`}}l 5 jl`ablrczkl( L} treml} m`amua`jl} uzcacw`k l} y`alre} }ckua`jl} t`r` `kl}zr` ze}ze

    jl `zcyl }Z&0!(((!}Z&=4! lu }eg`! l treml j` ltml e m`amua`jl mlk l y`alr jl `zcyl

    treyc`kehze mlhnemcjl( L y`alr je O] .achn` yerje# ilc m`amua jl ` t`rzcr j`}

    kejc`} j` jc}zrcoucml `kl}zr`a t

    O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4#

    e

    l} chzery`al} mlk 35% je mrejcocacj`je .achn`} yerkean`} zr`meg`j`}#! ` t`rzcr jl}

    pu`hzc} p4(4?5 e p4(325( @ achn` e}mur` jeh}` }l l} treml} j` ltml .lZ&0!((((!lZ&=4#!

    }ckua`jl} h` }eml :(0 mlkl `kl}zr` ze}ze t`r` ` ltml(

    =:

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    53/118

    Icbur` :(047 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl }ckua`jl t`r` ` `kl}zr` ze}ze + kljeal

    o(

    =4 Jc`}

    Lz

    4 5 04 05 ?4 ?5 =4

    ?

    9

    04

    _e`a Treyc}zl CM 35%

    L} re}uaz`jl} j` jc}zrcoucml `kl}zr`a t.O].}Z&0! ?! j ;

    =4#!(((!O].}Z&=4! ?! j ; 4##! t }}l 5 jl `ablrczkl! e}zl `tre}ehz`jl} h`

    ffbur` :(04( @ tremcffm`ml uzcacw` l} y`alre} jl `zcyl pue ilr`k treyc}+

    zl} hl t`}}l 5 jl `ablrczkl( L} treml} .achn` yerje# }l `} kejc` je

    t.O].}Z&0! ?! j ; =4#!(((!O].}Z&=4!

    ?! j ; 4## e l} chzery al} mlk 35% je

    mrejcocacj`je .achn`} yerkean`} zr`meg`j`}#! }l l} pu`hzc} p4(4?5 e p4(325( @ achn`

    e}mur` jeh}` }l l} treml} }ckua`jl} j` ltml .lZ&0!((((!lZ&=4# ber`jl} h` }eml

    :(0(

    Icbur` :(007 Ltml }ckua`j` t`r` `kl}zr` ze}ze! tremcffm`ml tlr O] e chzery`al}

    mlk 35% je mrejcocacj`je! uzcacw`hjl l `zcyl treyc}zl hl t`}}l 5 + kljeal o(

    =4 Jc`}

    L

    z

    4 5 04 05 ?4 ?5 =4

    4

    5

    05

    _e`a Treyc}zl CM 35%

    =5

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    54/118

    :(?(? Yla`zcacj`je Chy rc`hze mlk Chilrk`ml jl _ezlrhl e

    je Ju`} Ltmle} + Kljeal m

    Sz ; &

    zz .:(0=#

    L0z ; O].?! Sz# & 0 0z .:(0:#

    L?z ; O].?! Sz# & ? ?z! z! 0z! ?z H.4! 0# .:(05#

    E}z` }eml `tre}ehz` uk kljeal! lhje }l uzcacw`j`} ju`} ltmle} jcierehze} je

    uk ke}kl `zcyl( Ek mlkt`r`ml `l kljeal o! `tre}ehz`jl h` }eml `hzerclr!

    ` jcierehm` e}z h` chmau}l je k`c} uk` epu`ml retre}ehz`jl luzr` ltml jlke}kl `zcyl( E}ze kljeal e klzcy`jl teal b`hnl je tremc}l j` jc}zrcoucml `

    tl}zerclrc je ? h` }eml `hzerclr( @ epu`ml t`r` l} rezlrhl} hl ch}z`hze z .:(0=#

    e ` ret`r`kezrcw`ml j` epu`ml .?(0=#! lhje Sz ; ah.]z&0,]z# H.! z?# e ; . ?,?#z e l y`alr e}ter`jl t`r` l} alb+rezlrhl}( @ epu`ml .:(0:# re+tre}ehz` l} treml} j` ltml hukerl uk hl ch}z`hze z! L0z H.O].Sz! ?#! ?0 # e `epu`ml .:(05# l} treml} j` ltml hukerl ? hl ch}z`hze z! L?z H.O].Sz! ?#! ?0 #(@ chmau}l je k`c} uk` epu`ml cktacm` hl `mre}mckl je k`c} uk` jc}zrcoucml d

    }er e}zck`j`(

    @ jc}zrcoucml tl}zerclrc mlhguhz` t.qSZ! L0Z! L?Z# tlje }er m`amua`j` je `mlrjlmlk ` epu`ml :(09! lhje ; .! ?! ?0 !

    ??

    # }l l} t`rkezrl} ehylaycjl}( L}

    yezlre} SZ ; .s0!(((!sZ#! L0Z ; .l00!(((!l0Z# e L?Z ; .l?0!(((!l?Z#! retre}ehz`k

    chilrk`ml jl} rezlrhl}! ltml 0 e ltml ?! re}temzcy`kehze( @} jc}zrcoucmle} `

    trclrc trltl}z`} t`r` e}ze kljeal }l H.k ! R?#! ? BC.`! o#! ?0 BC.m! j#e ?? BC.e! i#(

    t.qSZ! L0Z! L?Z# ;Zz;0

    t.l0zqsz! ?! ?0 #t.l?zqsz! ?! ?? #t.szq! ?#t.#

    .:(09#

    L} `ablrczkl} u}`jl} t`r` e}zck`r l} t`rkezrl} je}ze kljeal }l! @kl}zr`jlr

    je Bcoo} e Kezrltlac} N`}zchb}( @}}ck mlkl lmlrrcjl hl kljeal o! ` jc}zrcoucmlmlhjcmclh`a mlktaez` t`r` ? hl `tre}ehz` ilrk` mlhnemcj`(

    =9

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    55/118

    @} jc}zrcoucmle} mlhjcmclh`c} mlktaez`} je ! ?0 ! ??

    e ?7

    q? HRsZ & kz

    Z R & z!

    Rz?

    Z R & z .:(02#

    ?0q? BC

    Z & ?m

    ?!

    Zz;0

    l0z O].sz! ?#

    ?& ?j

    ?

    .:(0>#

    ??q? BC

    Z & ?e

    ?!

    Zz;0

    l?z O].sz! ?#

    ?& ?i

    ?

    .:(03#

    t.?q! ?0! ??# ?.Z? &

    0?&`&0# e~t

    P0

    ??Rz

    e~t

    P? & P=

    ??0 ??

    .:(?4#

    lhje7 P0 ; RZz;0

    .sz #? & z.k#? & ?R oz

    P? ; ??

    Zz;0

    l0z O].s!?#

    ?e P= ;

    ?0

    Zz;0

    l?z O].sz! ?#

    ?

    @ jc}zrcoucml trltl}z` .:(?0# e uk` B`k` Chyer}`! t`rze j` jc}zrcoucml mlhjc+

    mclh`a mlktaez` t.?q! ?0! ??#( Uzcacw`r uk` trltl}z` pue }eg t`rze jl humaelj` mlhjcmclh`a mlktaez` e uk kezljl kuczl uzca( C}zl `ukehz` ` z`~` je `mecz`ml

    jl `ablrczkl e i`w ` m`jec` mlhyerbcr k`c} rtcjl(

    ?q BC

    Z & 0 & ?`

    ?!

    P0?Rz

    .:(?0#

    lhje7 P0 ; RZ

    z;0.sz #? & z. k#? & ?R oz

    @ trchmct`a jcierehm` ehzre l} kljeal} o e m lmlrre h` trlo`ocacj`je je `mecz`ml

    jl `ablrczkl Kezrltlac}+N`}zchb}! pue uzcacw` ` chilrk`ml `breb`j` tea`} ltmle} 0

    e ?(

    T.?.c#! ?.c&0## ; kch

    0!

    .:(??#

    lhje7 ;

    e~t

    0

    ??0??

    ??

    Z

    z;0 l0z O].sz! ?.c&0##

    ?

    & ??

    Z

    z;0 l?z O].sz! ?.c&0##

    ?

    e~t

    0

    ??0??

    ??

    Zz;0

    l0z O].sz! ?.c##

    ?& ??

    Zz;0

    l?z O].sz! ?.c##

    ?

    =2

  • 7/31/2019 MODELOS PARA PRECIFICAO DE OPES: UMA ABORDAGEM BAYESIANA PARA ESTIMAR A VOLATILIDADE

    56/118

    ]ckua`ml

    @ `y`ac`ml jl kljeal m ilc iecz` ` t`rzcr je y`alre} ber`jl} `rzcffmc`akehze! uzc+

    acw`hjl ek br`hje t`rze l mlhguhzl je j`jl} }ckua`jl} h` }eml `hzerclr( L}

    treml} t`r` l `zcyl ber`jl} je `mlrjl mlk ` epu`ml ?(0= e t`rkezrl} ; 4(9>

    e ? ; 4(??( L} treml} j` ltml 0 L0Z ; .l00!(((!l0Z#! }ckua`jl} je `mlrjl mlk

    ` epu`ml= :(= mlk t`rkezrl}7 treml je e~ermmcl F0 ; _*:5! 44! yla zcacj`je

    ? ; 4(??! z`~` je gurl} acyre je rc}ml r ; 00(?5%! .Z+z# jc`} t`r` l yehmckehzl!

    mlk Z;0=4 e t`rkezrl ?0 ; 4(?(

    T`r` re`acw`r ` }ckua`ml uzcacw`hjl l kljeal m e heme}}rcl ber`r treml} t`r`

    uk` }ebuhj` ltml L?Z ; .l?0!(((!l?Z#! ` ltml ilc }ckua`j` j` ke}k` ilrk` pue

    ` j` }eml `hzerclr uzcacw`hjl uk treml je e~ermmcl F? ; _*:>! 44 e uk t`rkezrl

    ?? ; 4(05(

    Ltmle} je uk ke}kl `zcyl! mlk uk ke}kl zektl je ycj` jcierek `teh`} ek }eu

    treml je e~ermmcl e y`rc`ml( ]ehjl l trckecrl uk t`rkezrl mlaez`jl jcrez`kehze

    jl kerm`jl! ehpu`hzl pue l }ebuhjl tremc}` }er e}zck`jl( Uk e~ektal jc}zl tlje

    }er yc}zl h` ffbur` :(0?!