A Trader’s Approach for a Retail Investor · A Trader’s Approach for a Retail Investor Option Fundamentals . 2 Fundamentals Strategies Managing positions ... •Advanced Trading

Rajib Ranjan Borah & Nitesh Khandelwal

QuantInsti Bangkok, 6 Oct 2014

Option Trading Techniques: A Trader’s Approach for a Retail Investor

Option Fundamentals

2

Fundamentals

Strategies

Managing

positions

Sophistication

through

automation

Topics

3

Topics

• Understanding basics of options

and derivatives

Fundamentals

Strategies

Managing

positions

Sophistication

through

automation

4

Topics

• A Few Simple Option Trading Strategies

Fundamentals

Strategies

Managing

positions

Sophistication

through

automation

5

Topics

• Initiating and Managing Option Positions

• Handling risks – different risk management parameters

Fundamentals

Strategies

Managing

positions

Sophistication

through

automation

6

Topics

Fundamentals

Strategies

Managing

positions

Sophistication

through

automation

• Advanced Trading Strategies

• Complex Position Management using Automation

7

Definitions

– Derivative is a financial instrument whose price is derived from the price of some other financial instrument.

– Option is a special type of derivative instrument - the buyer of the option has the option (i.e. right but not the obligation) to buy/sell a specified amount of underlying asset at a specified price on or before a specified date

– Other types of common derivatives: Future: the owner of such a derivative is obligated to buy/sell a specified

amount of underlying asset at a specified price on a specified date

Forward: Similar to futures, but traded OTC instead of in the exchange

Fundamentals Strategies Position Management Automation & Sophistication

8

• Two types of options – Call Options: Buyer has the option (but not the obligation) to buy the underlying

– Put Options: Buyer has the option (but not the obligation) to sell the underlying

• Defining Characteristics of Option Instruments – Strike: Price of the underlying at which the option can be exercised

– Expiry Date: The date at which the option can be exercised

– Premium: Upfront payment made by the buyer of the option (to the seller)

• Option Styles – European: can be exercised only on expiry date

– American: can be exercised anytime prior to expiry date

– Exotic – Bermudan, Asian, Binary, Barrier, etc


Option Types

9

CALL OPTION PUT OPTION

B

U

Y

E

R

S

E

L

L

E

R

The right

(but not the obligation)

to buy

The right

(but not the obligation)

to sell

The potential obligation

to buy The potential obligation

to sell

Option Types Elaborated


10

Payoff from holding a call option instrument

Consider a Call Option on XYZ stock with strike = 30, expiry date = 30th August 201X

At Expiry the payoff of the call option for the buyer is as shown below:

Strike at 30

Will only exercise the

call option if underlying

at expiry is more than

the strike

0

2

4

6

8

10

12

14

20 22 24 26 28 30 32 34 36 38 40 42

Underlying price at expiry

For e.g., if the

underlying price is at

36, the buyer of the

option can buy the

underlying at 30.

Hence, a payoff of 6.


11

Payoff from holding a put option instrument

Consider a Put Option on XYZ stock with strike = 30, expiry date = 30th August

201X.

At Expiry the payoff of the put option for the buyer is as shown below:

0

2

4

6

8

10

12

20 22 24 26 28 30 32 34 36 38 40 42

Strike at 30

For e.g., if the

underlying price is at

23, the buyer of the

option can sell the

underlying at 30.

Hence, a payoff of 7.

Will only exercise the

call option if underlying

at expiry is less than

the strike


12

12

-4

-2

0

2

4

6

8

10

12

20 22 24 26 28 30 32 34 36 38 40 42


Payoff - Buy Call Option

Premium

Breakeven Point

-12

-10

-8

-6

-4

-2

0

2

4

20 22 24 26 28 30 32 34 36 38 40 42


Payoff - Sell Call Option

-4

-2

0

2

4

6

8

10

20 22 24 26 28 30 32 34 36 38 40 42

Underlying Price at Expiry

Payoff - Buy Put Option

-10

-8

-6

-4

-2

0

2

4

20 22 24 26 28 30 32 34 36 38 40 42

Payoff - Sell Put Option

Premium Strike


13

Moneyness

Terminology Call Option Put Option

In the Money (ITM) Underlying Price > Strike Underlying Price < Strike

At the Money (ATM)

Underlying Price = Strike Underlying Price = Strike

Out the Money (OTM)

Underlying Price < Strike Underlying Price > Strike


14

Option Premium (price) components:

• Option price = Intrinsic Value + Time Value

– Intrinsic Value: Immediate value of the option given the current relationship between the price of underlying and the price of the option

• For call options, intrinsic value = underlying – option strike

• For put options, intrinsic value = option strike - underlying

– Time Value: Because the buyer of the option has the upside benefits but not downside obligations, therefore future price movements in the underlying can benefit (but not harm) the buyer – therefore there is an additional value for the option instruments for the extra benefits future price movements might bring

• An option with no intrinsic value is an Out of The Money Option


15

Option Pricing Methodology

• Pricing depends on key characteristics of instrument

– Option Strike

– Option Expiry date

– Current Underlying Price

– Characteristics of price change in underlying (volatility, price jumps, etc)

– Interest Rate & Stock Borrowing Rates

– Dividends

– Option type (Call/Put)

– Option Style (American/European)


16

Option Pricing Methodology

• Common Pricing Formulations

Underlying Characteristic Pricing Methodology Constant Volatility Black Scholes Constant Volatility with Dividends Black Scholes Merton Constant Volatility with Poisson Jumps Merton Jump Diffusion Volatility as a function of Underlying price CEV Volatility as a function of Underlying price & time to expiry

Derman Kani

Volatility is volatile Heston American type expiry Barone Adesi Whaley, Bjerksund Stensland Currency Options Garman Kohlhagen


17

Thank You

Merci

Danke

Gracias

Arigato

Asante

Grazi

Shukriya

[email protected] / +91 – 9920 – 44 - 88 – 77 / +65 – 6549 – 7213

Go Algo! Join QI’s EPAT (Executive Program on Algorithmic Trading)!


Question & Answers

mailto:[email protected]

Global Trends in Option Trading


QuantInsti Bangkok, 6th October 2014

Options Trading Techniques:

A Trader’s Approach for a Retail Investor

How do you decide: where to trade?

As a trading manager, how do you decide which geographies to trade ?

Relevant factors for analyzing different markets → Current landscape in different geographies → QA

As a trading manager, how do you decide which geographies to trade ?



As a trading manager, how do you decide which geographies to trade ? – Am I allowed to trade in that country (i.e. how conducive are regulations) ?




• Are foreigners allowed to trade ?

• Are there restrictions on position-sizing / short-selling ?












– Are these markets interesting to trade ?






– Are these markets interesting to trade ? • What are the listed instruments ?

• What is the volume traded ?








– Will I be able to make profits ?








– Will I be able to make profits ? • What is the level of sophistication of competition ?

• Who are the leading players ?










– What are the complexities to connecting to these markets ? • Technological protocols used by these exchanges – common standard protocols OR unique

custom protocols

• Brokers to connect to these markets











custom protocols












custom protocols



Regulations










custom protocols



Regulations

Market Size










custom protocols



Regulations

Market Size

Competition










custom protocols



Regulations

Market Size

Competition

Technology










custom protocols



Regulations

Market Size

Competition

Technology


Trading in various landscapes


Equity volumes – avg monthly volumes (USD million)

Americas

Bermuda SE 4

BM&FBOVESPA 67,550

Buenos Aires SE 279

Colombia SE 2,162

Lima SE 338

Mexican Exchange 14,780

NASDAQ OMX 798,729

NYSE Euronext

(US) 1,141,704

Santiago SE 3,640

TMX Group 114,290

Total region 2,143,474

APAC

Australian SE 73,463

BSE India 7,046

Bursa Malaysia 12,323

Colombo SE 130

GreTai Securities Market 11,241

HoChiMinh SE 869

Hong Kong Exchanges 110,281

Indonesia SE 9,664

Japan Exchange Group - Osaka 17,594

Japan Exchange Group - Tokyo 525,411

Korea Exchange 107,050

National Stock Exchange India 39,913

New Zealand Exchange 752

Philippine SE 3,889

Shanghai SE 310,927

Shenzhen SE 321,542

Singapore Exchange 23,410

Taiwan SE Corp. 51,996

The Stock Exchange of Thailand 31,335

Total region 1,658,838

Europe

Athens Exchange 1,981

BME Spanish Exchanges 74,464

Budapest SE 869

Casablanca SE 263

Cyprus SE 3

Deutsche Börse 111,212

Irish SE 1,206

Ljubljana SE 33

Luxembourg SE 12

Malta SE 6

Moscow Exchange 20,167

NASDAQ OMX Nordic Exchange 52,153

NYSE Euronext (Europe) 138,490

Oslo Børs 10,200

SIX Swiss Exchange 56,413

Wiener Börse 2,154

Total region 469,626

MEA: Middle East + Africa

Abu Dhabi SE 1,816

Amman SE 285

Borsa Istanbul 34,947

Cyprus SE 3

Egyptian Exchange 1,077

Irish SE 1,206

Johannesburg SE 28,608

Kazakhstan SE 58

Mauritius SE 26

Muscat Securities Market 478

Qatar Exchange 1,714

Saudi Stock Exchange - Tadawul 30,202

Tel Aviv SE 4,475

Total region 104,895


Index FO – annual volumes (USD million)

Americas Options Future

BM&FBOVESPA 238 119.0 504 342.0

Bourse de Montreal 3 550.8 555 764.0

CBOE Future Exchange x NA

Chicago Board Options Exchange NA x

CME Group 9 987 400.0 46 628 400.0

Colombia SE x 19.2

ICE Futures US 6 516.0 2 962 600.0

International Securities Exchange NA NA

MexDer 1 761.5 30 896.1

NASDAQ OMX (US) NA NA

NYSE Euronext (US) NA NA

APAC Options Future

ASX Derivatives Trading 441 915.0 2 561.6

ASX SFE Derivatives Trading 46 330.5 1 204 770.0

Bombay SE 1 168 300.0 10 210.9

Bursa Malaysia Derivatives NA 71 423.6

China Financial Futures Exchange NA 22 909 400.0

Hong Kong Exchanges 1 838 560.0 4 539 370.0

Korea Exchange 67 864 200.0 5 855 830.0

National Stock Exchange India 4 668 890.0 498 918.0

Osaka SE NA 7 468 830.0

Shanghai Futures Exchange 0.0 0.0

Singapore Exchange NA NA

TAIFEX 1 485 740.0 1 480 410.0

Thailand Futures Exchange NA NA

Tokyo SE Group NA 2 630 990.0

EMEA Options Future

Athens Derivatives Exchange 432.3 28 113.5

BME Spanish Exchanges 60 489.2 672 335.0

Borsa Istanbul 35.1 63 631.4

Budapest SE 0.0 341.8

EUREX 13 764 800.0 18 691 000.0

ICE Futures Europe 0.0 0.0

Johannesburg SE 2 946.5 487 400.0

Moscow Exchange 118 079.0 752 618.0

NYSE.Liffe Europe 3 297 390.0 6 282 720.0

OMX Nordic Exchange 151 241.0 573 599.0

Oslo Børs 439.1 1 752.9

Tel Aviv SE 641 250.0 976.1

Wiener Börse 56.2 22 030.8


Equity FO – annual volumes (USD million)


BM&FBOVESPA 994 498.0 NA

Bourse de Montreal 73 960.1 0.0

Buenos Aires SE NA NA

Chicago Board Options Exchange NA NA

Colombia SE NA 480.6

International Securities Exchange NA NA

MexDer 90.0 13.4

NASDAQ OMX (US) NA NA

NYSE Euronext (US) 104 464.0 NA

BM&FBOVESPA 994 498.0 NA

Bourse de Montreal 73 960.1 0.0

APAC Options Future

ASX Derivatives Trading 284 474.0 11 867.0

Bombay SE 3 076.7 7 442.2

Hong Kong Exchanges 167 335.0 1 485.5

Korea Exchange 0.0 56 761.0

National Stock Exchange India 416 644.0 811 791.0

New Zealand 0.0 NA

Osaka SE NA NA


TAIFEX 177.6 22 743.6


Tokyo SE Group NA NA

EMEA Options Future

Athens Derivatives Exchange 17.0 2 450.0

BME Spanish Exchanges 31 668.0 15 271.2

Borsa Istanbul 14.4 11.9

Budapest SE 0.0 2 684.7

EUREX 784 435.0 752 475.0

ICE Futures Europe 0.0 0.0

Johannesburg SE 311.3 16 625.5


NYSE.Liffe Europe 343 406.0 455 497.0

OMX Nordic Exchange 52 967.4 4 658.3

Oslo Børs 1 874.3 1 836.7

Tel Aviv SE 4 335.2 NA

Wiener Börse 307.0 0.0


Currency – annual volumes (USD million)


BM&FBOVESPA 435 060.6 4 196 493.1

Bourse de Montreal 68.2 0.0

CME Group 2 076 378.0 25 281 026.0

Colombia SE NA 10 674.9

ICE Futures US 3 410.0 658 019.0

MexDer 181.9 135 749.3

APAC Options Future

Hong Kong Exchanges NA 13 948.8

Korea Exchange NA 532 393.2

National Stock Exchange India 252 897.5 614 399.2

Osaka SE NA 61 932.8


EMEA Options Future

Borsa Istanbul NA 4 658.1

Johannesburg SE 8 934.8 25 155.6


NYSE.Liffe Europe 2 324.6 37.3

Tel Aviv SE 108 322.8 0.0


Interest Rate – annual volumes (USD million)


BM&FBOVESPA 3 600 770.0 18 193 900.0

Bourse de Montreal 569 518.0 23 217 400.0

Buenos Aires SE NA NA

CME Group 163 885

000.0 614 271

000.0

Colombia SE NA 32 850.9

MexDer NA 93 456.0


APAC Options Future

ASX SFE Derivatives Trading 393 778.0 47 596 300.0

Bombay SE NA NA

China Financial Futures Exchange NA 50 232.7

Hong Kong Exchanges NA 7.2

Korea Exchange NA 4 084 080.0

National Stock Exchange India NA NA


TAIFEX NA 2.2

Tokyo SE Group NA NA

EMEA Options Future

BME Spanish Exchanges 0.0 1 413.4

EUREX 11 544 400.0 76 220 100.0


London Metal Exchange NA NA

Moscow Exchange 0.0 5 323.7

NYSE.Liffe Europe 175 658 000.0 443 350 000.0

OMX Nordic Exchange 915 175.0 3 560 020.0

Tel Aviv SE NA NA


ETF – annual volumes (USD million)

Americas ETF ETF Opt

BM&FBOVESPA 11 366.8 138.7

Colombia SE 1 070.1

Lima SE 9.8

Mexican Exchange 104 903.9 1.8

NASDAQ OMX 6 695 703.4 NA

NYSE Euronext (US) 3 589 241.4 48 077.3

Santiago SE 117.1

TMX Group 73 824.8

Bourse de Montreal NA 5 123.0

CME NA NA

ISE NA NA

APAC ETF ETF Opt

Australian SE 7 487.3

BSE India 1 118.3

Bursa Malaysia 43.6

Hong Kong Exchanges 116 431.5 16 776.7

Indonesia SE 2.1

Japan Exchange Group - Osaka 73 386.2 NA

Japan Exchange Group - Tokyo 163 170.1 NA

Korea Exchange 178 724.6

National Stock Exchange India 2 132.8

New Zealand Exchange 59.6

Shanghai SE 109 240.5

Shenzhen SE 36 707.2

Singapore Exchange 2 591.1

Taiwan SE Corp. 9 496.8

The Stock Exchange of Thailand 250.3

EMEA ETF ETF Opt

Athens Exchange 14.7

BME Spanish Exchanges 5 732.2

Borsa Istanbul 4 350.9

Budapest SE 1.9

Deutsche Börse 162 958.7

Irish SE 19.3

Johannesburg SE 5 624.3 ~ 0

Ljubljana SE 0.0

Luxembourg SE 0.0

NASDAQ OMX Nordic Exchange 15 593.7

NYSE Euronext (Europe) 100 747.8

Oslo Børs 4 736.7

Saudi Stock Exchange - Tadawul 18.6

SIX Swiss Exchange 98 074.8

Wiener Börse 5.3


Commodity– annual volumes (USD million)


BM&FBOVESPA 602.9 21 666.2

CME Group 10 561

200.0 47 823 300.0

Colombia SE NA 6.6

ICE Futures Canada 47.4 57 599.8

ICE Futures US 305 023.0 1 347 450.0


APAC Options Future

ASX SFE Derivatives Trading 5 284.0 17 687.1

Bursa Malaysia Derivatives NA 151 944.0

Dalian Commodity Exchange NA 7 676 520.0

Korea Exchange NA 161.1

New Zealand 0.0 132.1

Shanghai Futures Exchange NA 9 852 290.0

TAIFEX 717.9 1 146.7

Zhengzhou Commodity Exchange NA 3 074 910.0

EMEA Options Future

Borsa Istanbul NA 807.7

Budapest SE 0.0 138.5

ICE Futures Europe 31 495.0 29 469 200.0


London Metal Exchange 663 968.0 13 965 900.0

Moscow Exchange 309.6 46 291.3

NYSE.Liffe Europe 1 918.0 403 586.0

Q & A


Copyright © 2014 by QuantInsti Quantitative Learning Private Limited.

Although great care has been taken to ensure accuracy of the information

in this presentation – however the author (and QuantInsti) accepts no

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statement, estimate or opinion. QuantInsti also accepts no liability for the

consequences of any actions taken on the basis of the information

provided.

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Prior approval from QuantInsti is necessary before usage of this

presentation for educational and (or) commercial purposes.

This document provides an outline of a presentation and is incomplete

without the accompanying oral commentary and discussion.

Disclaimer


QuantInsti Bangkok, 6 Oct 2014

Option Trading Techniques: A Trader’s Approach for a Retail Investor

Option Trading Strategies

Directional strategies:

• Long / short call • Long / short put

• Long / short call(/bull) spread

• buy lower strike, sell higher strike

• Long / short put(/bear) spread • sell lower strike, buy higher strike

• Long / short combo

• call at higher strike, put at lower

Option Strategies – basic strategies Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Volatility strategies:

• Long / short straddle • Put and call of same strike

• Long / short strangle • OTM Put and call of different strikes

• Long / short gut • ITM Put and call of different strikes

• Long / short butterfly

• Buy wings and sell ATM – or vice versa • Long / short condor

• Buy farther away OTMs and sell nearest OTMs – or vice versa

• Long / short iron butterfly • Buy straddle & sell strangle


Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Time Value strategies:

• Long / short calendar spread (a.k.a. horizontal trades) • Sell near expiry options, buy far expiry

options

• Long / short diagonal calendar spread • Same as above but different strikes

• Interest Plays • Sell underlying and deep ITM puts • Earn interest on cash from selling


Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Hedging strategies

• Protective Calls • Short underlying hedged using long OTM call

• Protective Puts • Long underlying hedged using long OTM put

• Covered Call Writes • Long underlying to cover short OTM call • Short underlying to cover short OTM put

• Fences or Collars • Combining Protective option with covered writes Long Underlying + Long OTM puts + short OTM

calls


Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Backspread (also known as ratio backspread / long ratio

spread)

• Delta neutral spread consisting of more long options than short • Options with lower delta purchased • Options with higher delta sold

Ratio Vertical Spread (also known as ratio spread, short ratio spread, vertical

spread or front spread) • Basically the opposite of backspreads

• Options with higher delta purchased • Options with lower delta sold

Option Strategies – volatility spreads Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Volatility Curve Skew Trades

• Risk Reversal (a.k.a. risky)

• Long OTM calls + Short OTM puts • Often a bet on vol curve skew

Advanced Volatility Spreads:

• Forward Volatility Based Spreads • Volatility for forward periods

Option Strategies – volatility spreads Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

• Conversal: • Synthetically short underlying + long

underlying • (Short call + long put) + long

underlying

• Reversal: • Synthetically long underlying + short

underlying • (Long call + short put) + short

underlying

• In both cases, risks are minimal (Except dividend & interest rates exposures. Or pin risks for stock settled options)

Option Strategies – simple option arbitrages Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

• Dispersion:

• Index constituted of a basket of stocks • Implied volatility of index options should

therefore be linked to implied volatility of stock options (of stocks making up the index)

• Dispersion trading is a way to trade “Implied Correlation” between volatility of index and index components i.e. bet on the degree to which constituent

stocks disperse

Option Strategies – correlation & dispersion Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

• Dispersion (contd) • The volatility of a basket with two assets is

• Where ρ is the correlation coefficient • Volatility of a basket with ‘n’ assets will be

• Instead of n.(n-1)/2 correlations for a basket of n stocks, define a single average correlation


Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

• The strategy becomes: • Buy index volatility & sell component

volatility when correlation is towards lower band

• Do reverse when correlation is towards upper band


Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Option Strategies – advanced option arbitrages Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

• Dividend Plays • Buying underlying and selling deep ITM

calls

• Skew Dividends • Dividend expectations at different

underlying levels

Option Strategies – advanced option arbitrages

• Boxes: • A conversal at one exercise price/strike • A reversal at another exercise price/strike

• Long box = • Synthetically long the lower exercise price • Synthetically short the higher exercise price

• What would be the price of a 90/100 box ? • Value of box at expiry (=10) – carrying costs

• Often cheaper way of borrowing funds from

the market

Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

Option Strategies – advanced option arbitrages Directional

Volatility

Time Value

Hedging

Volatility Spreads

Option Arb

Correlation

Dividend

Borrowing Tool

• Jelly Rolls: • A synthetic long position in one expiry • A synthetic short position in another expiry

• Long jelly roll = • Synthetically long the near expiry options • Synthetically short the far dated expiry

options

• What would be the price of a 90/100 Jun/Sep jelly roll? • Value of roll = cost of holding underlying for

the 3 month period from Jun to Sep.


QuantInsti

Bangkok 06 Oct 2014

Managing Option Portfolios

Options Trading Techniques:

A Trader’s Approach for a Retail Investor

2

• First order risks: – Delta – i.e. change in option price with change in underlying price

– Vega – i.e. change in option price with change in underlying volatility

– Theta – i.e. change in option price as time to expiry reduces

– Rho – i.e. change in option price with change in interest rates

• Second Order risks – Gamma ( change of Delta with change in Underlying price)

– Vanna ( change of Delta with change in Volatility)

– Charm ( change of Delta with change in Time)

– Vomma ( change of Vega with change in Volatility)

– Veta ( change of Vega with change in Time)

– Change of Vega with change in Underlying price

– Vera (change of Rho with change in Volatility)

Risk Evaluations

3

• Third order risks: – Color (change of Gamma with change in Time)

– Speed (change of Gamma with change in Underlying Price)

– Zomma (change of Gamma with change in Volatility)

– Ultima (change of Vomma with change in Volatility)

• Other risks – Rega - Volatility curve skew

– Sega - Volatility curve wings

– Forward Volatility (Volatility between two expiry periods)

– Skewed gamma (change in Gamma with change in volatility curve skew)

– Skewed delta (change in Delta with change in volatility curve skew)

Risk Evaluations

4

Price of Call Option vs Price of Underlying

4

Options price is dependent on price of underlying

5

• The Hedge Ratio

• Equivalent Underlying Position

• Rate of change of price of option to change in underlying

• Probability of option finishing in the money

5

Delta

6

• i.e. Delta is dependent on • underlying price,

• time to expiry

• volatility

6

Delta

7

Delta vs Underlying price/Moneyness

7

Delta vs Underlying Price

8

Call Delta vs Time left to expiry

8

Delta vs Time

9

Put Delta vs Time left to expiry

9

Delta vs Time

10

Combined Visualization

10

Delta vs Underlying Price & Time

11

Call Delta vs Volatility

11

Delta vs Volatility

12

Put Delta vs Volatility

12

Delta vs Volatility

13

• As we have seen, deltas change with underlying price (more so towards expiry)

• Gamma is the second derivative of the change of option price with respect to change in underlying price

• = ∂2C/∂S2 = ∂Δ/∂S = N’(h)/ (Sσ√t)

13

Gamma

14

Gamma vs Price of Underlying

14

Gamma vs Price of Underlying

15

Gamma vs Time

15

Gamma vs Time / Volatility

16

Overall impact

16

Gamma vs Underlying Price & Time / Volatility

17

Gamma vs Volatility

17

Gamma vs Time / Volatility

18

• Delta is a poor estimate because unit change in underlying varies from underlying to underlying

• Lambda gets change in option price to a percentage change in the underlying

18

Lambda / Gearing

19

• Rate of change of price with respect to strike • Strike 100, price = 10

• Strike 120, price = 12

• Dual delta = (12-10)/(120-100) = 2/20 = 0.1

• Relationship between delta & Dual Delta • Delta = 1/ Stock Price * (Option Price –

Strike * DualDelta)

19

Dual Delta

20

• Change in Gamma with respect to change in underlying

• Also known as gamma of the gamma

20

Speed

21

• Change in Gamma with respect to change in time

• As seen previously: color is highest near the date of expiry and for ATM strikes

21

Color / Gamma decay

22

• Change of option price with respect to change in volatility

• = ∂C/∂σ

• = S √t N’(h)

• = ∂P/∂σ

22

Vega

23

Option price at different volatility levels

23

Option Price vs Volatility

24

Vega at different strikes

24

Vega vs Underlying Price

25

Vega of an option with varying time left to expiry

25

Vega vs Time

26

Sensitivity to volatility is sensitive to volatility itself

26

Vega vs Volatility

27

27

Vega vs Underlying Price & Time/Volatility

28

• Long call or long put = Long vega

= Long gamma as well

• Long vega & long gamma require volatility to profit

• Vega = S√t N’(h)

= S√t N’(h) . √tσSN’(h) / (√tσSN’(h))

= S√t N’(h) . √tσS/N’(h) .(N’(h) / (√tσS))

= S√t N’(h) . √tσS/N’(h) .(Gamma)

= S2tσGamma

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Vega & Gamma

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• Different expirations will react differently to changes in perception of future volatility • Long term volatility expectation is fairly

stable but short term is not

• Vegas for different months need to be weighted differently to get net vega across expiries

• Modified Vega =

• How to calculate Weightages ?

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Calibrating different Vegas

n

i

ii WeightageVega1

.

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• How to calculate Weightages ?

• Empirical (based on observed historical volatility for different time periods)

– Theoretical/ square root weightages. Weightages proportionate to

–But is being weighted neutral enough?

– Forward volatilities

30

Calibrating different Vegas

Documents

A Trader’s Approach for a Retail Investor · A Trader’s Approach for a Retail Investor Option Fundamentals . 2 Fundamentals Strategies Managing positions ... •Advanced Trading