Manage Complex Option Portfolios: Simplifying Option Greeks Part II
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1 Manage Complex Option Portfolios: Simplifying Option Greeks Part II Monday, 11 th September 7:30 PM IST 2:00 PM GMT 10:00 AM EST A Pioneer Algo Trading Training Institute Streamlined Investment Management
2 About the Speaker Rajib Ranjan Borah Co-Founder & Director - QuantInsti Rajib manages the course segment on option derivatives and also works with exchanges, financial & educational institutions to design educational programs. He has conducted workshops and conferences in America, Europe and Asia. Rajib worked with leading HFT firm Optiver in Amsterdam on options derivatives market making & high frequency equity arbitrage strategies across all major European & US exchanges. Before Optiver, Rajib was a management strategy consultant with PricewaterhouseCoopers where he assisted a consortium in setting up a national commodity derivatives exchange. A national Olympiad finalist, Rajib has twice represented India at the World Puzzle Championships. He has a post-graduate management degree from the Indian Institute of Management Calcutta, a bachelor s degree in Computer Engineering from the National Institute of Technology Surathkal; and has internship experiences with Bloomberg in New York (equity option derivatives research) & with Solutia s EMEA strategy HQ in Belgium. 2
3 Delta Price of option from Black Scholes formula C t rt = SN( d 1) Xe N( d2) Delta = C/ S or ½( C/ S- + C/ S+) to be more precise = N(d1) d 1 = St ln( X 2 σ ) + ( r + ) t 2 σ t N( x) = 1 2π x e 2 z 2 dz 3
4 Delta i.e. Delta is dependent on: underlying price, time to expiry volatility 4
5 Gamma: Delta vs Underlying Price Call Delta vs Underlying Price Delta of option Call 90 Strike Call 100 Strike Call 110 Strike Underlying Price 5
6 Gamma: Delta vs Underlying Price Put Delta vs Underlying Price Delta of option Put 90 Strike Put 100 Strike Put 110 Strike Underlying Price 6
7 Charm: Delta vs Time Call Delta vs Time left to expiry Delta of option Call 90 Strike Call 100 Strike Call 110 Strike Underlying Price = 100 Volatility = 20% Days to Expiry 7
8 Charm: Delta vs Time Put Delta vs Time left to expiry Delta of option Put 90 Strike Put 100 Strike Put 110 Strike Underlying Price = 100 Volatility = 20% Days to Expiry 8
9 Vanna: Delta vs Volatility Call Delta vs Volatility Delta of option Call 90 Strike Call 100 Strike Call 110 Strike % 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% Implied Volatility 9
10 Vanna: Delta vs Volatility Put Delta vs Volatility 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% Delta of option Put 90 Strike Put 100 Strike Put 110 Strike Implied Volatility 10
11 Gamma 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) 11
12 Speed: Gamma vs Price of Underlying Gamma vs Price of Underlying Gamma of option Call 90 Strike Call 100 Strike Call 110 Strike Underlying Price 12
13 Color: Gamma vs Time Gamma vs Time Delta of option Days to Expiry Call 90 Strike Call 100 Strike Call 110 Strike 13
14 Zomma: Gamma vs Volatility Gamma vs Volatility Delta of option % 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% Implied Volatility Call 90 Strike Call 100 Strike Call 110 Strike 14
15 Vanna: Vega vs Underlying Price Vega at different strikes Vega of option Call 90 Strike Call 100 Strike Call 110 Strike Underlying Price 15
16 Veta: Vega vs Time Vega of an option with varying time left to expiry Vega of option Call 90 Strike Call 100 Strike Call 110 Strike Days to Expiry 16
17 Vomma: Vega vs Volatility Sensitivity to volatility is sensitive to volatility itself Vega of option Call 90 Strike Call 100 Strike Call 110 Strike % 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% Implied Volatility 17
18 Thega: Theta v/s Time to expiration Theta with changing time to expiry Theta K=100 K=110 K= Days to expiry 18
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Manage Complex Option Portfolios: Simplifying Option Greeks Part III
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55.444 Introuction to Financial Derivatives Week of December n, 3 he Greeks an Wrap-Up Where we are Previously Moeling the Stochastic Process for Derivative Analysis (Chapter 3, OFOD) Black-Scholes-Merton
DERIVATIVES AND RISK MANAGEMENT
A IS 1! foi- 331 DERIVATIVES AND RISK MANAGEMENT RAJIV SRIVASTAVA Professor Indian Institute of Foreign Trade New Delhi QXJFORD UNIVERSITY PRKSS CONTENTS Foreword Preface 1. Derivatives An Introduction
Introduction to Financial Derivatives
55.444 Introuction to Financial Derivatives Week of December 3 r, he Greeks an Wrap-Up Where we are Previously Moeling the Stochastic Process for Derivative Analysis (Chapter 3, OFOD) Black-Scholes-Merton