2012 금융수학 겨울학교 - FM 210 Mhz

February, 3 2012

FM 210 Mhz

과제결과발표2012.02.03.

금융수학 겨울학교

Contents

1 Option (1) Implicit method

(2) Stability by Von Neumann analysis

2. Network (1) Asset MST

(2) 3D simulation

3. Creative project (1) Paper introduction

(2) Future research

금융수학 겨울학교

PROF ILE

조이름

주소

창립 년도

직원 수

UNIST 테경관 210 호

2012. 2. 2.

총 4 명 | 수학 자갈 2 명 | 재무 천재 1 명 | 막내 ^.^

Staff

남자 1 호응용수학전공

여자 1 호응용수학전공

FM 210 (Finance & Math meet at Technomanagement building 210 class )

여자 2 호재무관리전공

여자 3 호테크노경영학부

(1)American

ca l l op t i on -

(2)Stability

(3)American

optionsVon Neumann analysis Operator splitting method

Mathmatical approach to op-tion

implicit method

(1) Discretize the Black-Scholes equation on n+1 time level using Taylor series expansion. Approximate the first-order spatial derivative at m-th grid point using m-1 and m grid points. Keyword : Taylor expansion

Taylor expansion

(1) Discretize the Black-Scholes equation on n+1 time level using Taylor series expansion. Approximate the first-order spatial derivative at m-th grid point using m-1 and m grid points. Keyword : Discretize

EU call option

Mathmatical approach to op-tion

(1)Ameri -can ca l l op t ion -

(2)Stability

(3)American

optionsVon Neumann analysis Operator splitting method implicit method

(2) Check stability in the sense the Von Neumann analysis.

Ke y w o rd : subst i tu t ing i n ex p l i c i t m e t h o d

(2) Check stability in the sense the Von Neumann analysis.

Ke y w o rd : s tab i l i t y i n ex p l i c i t m e t h o d

(2) Check stability in the sense the Von Neumann analysis.

Ke y w o rd : subst i tu t ing i n i m p l i c i t m e t h o d

(2) Check stability in the sense the Von Neumann analysis.

Ke y w o rd : expans ion

(2) Check stability in the sense the Von Neumann analysis.

Ke y w o rd : s tab i l i t y i n i m p l i c i t m e t h o d

Mathmatical approach to op-tion

(1)Ameri -can ca l l op t ion -

(2)Stability

(3)American op-

tions

Von Neumann analysis Operator splitting method implicit method

Asset t ree -

3D simula-tion

Paper in-troduction

Network approach to Finance

Net-work

with mathlab code Future research with mathlab code

Asset t ree -

3D simula-tion

Paper intro-duction

Network approach to Finance

Net-work

with mathlab code Future research with mathlab code

Int roduc t i on o f paper

1. The clustering of companies using the correlation matrix of asset returns,

2. Transforming correlations into distances,

3. Selecting a subset with the minimum spanning tree(MST) criterion.

-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t

Ma in theme o f paper

-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t

Asset Tree Asset Graph

Construction

Differences

Determining the minimum span-ning tree(MST) of the distances

Extracting the N(N-1)/2 distinct distance ele-ments from the upper triangular part of the

Order : fixed No cycles

Order : unfixed Cycles

Conc lus ion o f paper

-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t

In general, the tree and graph behave very similarly.

Second region – a straight line on the log-log plot G should decay more faster than T.

First region - in early timeT faster than G(∵G shows exponential de-cay)

G are far more optimal (shorter) than the T.

Log log g raph

-B a s e d o n Kosp i da ta

Network approach to Finance

Asset t ree -3D simula-

tionPaper in-

troduction

Net-work

with mathlab code Future research with mathlab code

Asset MST

Return = importdata('US_200001032008_STOCKReturn.mat'); Corr = corrcoef(Return); Dist = sqrt(2*(1-Corr)); Dist = triu(Dist) + triu(Dist)'; SDist = sparse(Dist); [out1 out2 out3 ] = mst(SDist); MST = [out1 out2 out3 ]; MST_Geometric_SUB02_Application(MST,'a');

Asset MST

Asset MST

과독점에 대한정부 규제 방법 ?

Network approach to Finance

Asset t ree -

3D simulationPaper in-troduction

Net-work

with mathlab code Future research with mathlab code

3D simulation

3D simulation

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0.5

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2003

2004

2005

2006

2007

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-1012002 2002.5 2003 2003.5 2004 2004.5 2005 2005.5 2006 2006.5

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3D simulation

Clear all; close all; clf;

SAME CODE

Futu re Research

-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t

1. 다른 주식과 많은 연결개수를 갖는 주식의 시장지수에 따른 공통속성의 정도와 개별속성의 정도 차이 .

2. 주식 간의 연결개수에 영향을 미치는 요인에 대한 분석 ( 연구 )

3. 주식들과의 연결개수에 따라 2 가지 이상의 집단으로 구분 후 , 평균비교 T 검정과 ANOVA 를 이용하여 집단간 통계적 유의한 차이를 보이는 특징에 대해 분석한다 .

4. 기업의 연결개수에 따른 수익성을 예측하기 위해서 회귀분석을 실시하여 , 베타 값에 따라 큰 영향을 미칠 수 있는지에 대한 분석 .

감사합니다