An Option Greeks Primer: Building Intuition with Delta Hedging and Monte Carlo Simulation using Excel

279 Pages·2015·29.223 MB·English

by  Jawwad Ahmed Farid

Global Financial Markets series
Global Financial Markets is a series of practical guides to the latest financial market
tools, techniques and strategies. Written for practitioners across a range of disciplines
it provides comprehensive but practical coverage of key topics in finance covering
strategy, markets, financial products, tools and techniques and their implementation.
This series will appeal to a broad readership, from new entrants to experienced prac-
titioners across the financial services industry, including areas such as institutional
investment; financial derivatives; investment strategy; private banking; risk manage-
ment; corporate finance and M&A, financial accounting and governance, and many
more.
Titles include:
Cyril Demaria
PRIVATE EQUITY FUND INVESTMENTS
New Insights on Alignment of Interests, Governance, Returns and Forecasting
Erik Banks
DARK POOLS, 2nd Edition
Off-Exchange Liquidity in an Era of High Frequency, Program, and Algorithmic
Trading
Erik Banks
LIQUIDITY RISK, 2nd Edition
Managing Funding and Asset Risk
Felix Lessambo
THE INTERNATIONAL CORPORATE GOVERNANCE SYSTEM
Audit Roles and Board Oversight
Sandy Chen
INTEGRATED BANK ANALYSIS AND VALUATION
A Practical Guide to the ROIC Methodology
Jawwad Farid
MODELS AT WORK
A Practitioner’s Guide to Risk Management
Frances Cowell
RISK-BASED INVESTMENT MANAGEMENT IN PRACTICE, 2nd Edition
Daniel Capocci
THE COMPLETE GUIDE TO HEDGE FUNDS AND HEDGE FUND STRATEGIES
Guy Fraser-Sampson
INTELLIGENT INVESTING
A Guide to the Practical and Behavioural Aspects of Investment Strategy
Michael Hünseler
CREDIT PORTFOLIO MANAGEMENT
A Practitioner’s Guide to the Active Management of Credit Risks
Ross K. McGill
US WITHHOLDING TAX
Practical Implications of QI and FATCA
David Murphy
OTC DERIVATIVES, BILATERAL TRADING AND CENTRAL CLEARING
An Introduction to Regulatory Policy, Trading Impact and Systemic Risk
Gianluca Oricchio
PRIVATE COMPANY VALUATION
How Credit Risk Reshaped Equity Markets and Corporate Finance Valuation Tools
Global Financial Markets series
Series Standing Order ISBN: 978–1–137–32734–5
(outside North America only)
You can receive future titles in this series as they are published by placing a standing order. Please
contact your bookseller or, in case of difficulty, write to us at the address below with your name and
address, the title of the series and the ISBN quoted above.
Customer Services Department, Macmillan Distribution Ltd, Houndmills, Basingstoke, Hampshire
RG21 6XS, England
An Option Greeks Primer –
Building Intuition with Delta
Hedging and Monte Carlo
Simulation Using Excel
Jawwad Ahmed Farid
Fellow Society of Actuaries
© Jawwad Ahmed Farid 2015
All rights reserved. No reproduction, copy or transmission of this
publication may be made without written permission.
No portion of this publication may be reproduced, copied or transmitted
save with written permission or in accordance with the provisions of the
Copyright, Designs and Patents Act 1988, or under the terms of any licence
permitting limited copying issued by the Copyright Licensing Agency,
Saffron House, 6–10 Kirby Street, London EC1N 8TS.
Any person who does any unauthorized act in relation to this publication
may be liable to criminal prosecution and civil claims for damages.
The author has asserted his right to be identified as the author of this work
in accordance with the Copyright, Designs and Patents Act 1988.
First published 2015 by
PALGRAVE MACMILLAN
Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited,
registered in England, company number 785998, of Houndmills, Basingstoke,
Hampshire RG21 6XS.
Palgrave Macmillan in the US is a division of St Martin’s Press LLC,
175 Fifth Avenue, New York, NY 10010.
Palgrave Macmillan is the global academic imprint of the above companies
and has companies and representatives throughout the world.
Palgrave® and Macmillan® are registered trademarks in the United States,
the United Kingdom, Europe and other countries
ISBN: 978–1–137–37166–9
This book is printed on paper suitable for recycling and made from fully
managed and sustained forest sources. Logging, pulping and manufacturing
processes are expected to conform to the environmental regulations of the
country of origin.
A catalogue record for this book is available from the British Library.
Library of Congress Cataloging-in-Publication Data
Farid, Jawwad Ahmed.
An option Greeks primer : building intuition with Delta hedging and Monte Carlo
simulation using Excel / Jawwad Farid.
pages cm.—(Global financial markets)
ISBN 978–1–137–37166–9 (hardback)
1. Options (Finance) 2. Hedging (Finance) 3. Finance – Mathematical models.
4. Monte Carlo method. 5. Microsoft Excel (Computer file) I. Title.
HG6024.A3F175 2015
332.64953—dc23 2014038793
For Amin, Salwa and Taha.
As promised.
May you be blessed with teachers
who broaden your minds and
change your lives.

Contents
List of Figures xi
Preface xx
Acknowledgements xxiv
About the Author xxvi
Glossary xxvii
Part I Refresher
Introduction: Context 3
1 O ptions 3
2 Option price drivers 3
3 G reeks 4
4 H edging and squaring 4
5 E mpirical and implied volatility 4
6 I n and out of money options 6
7 D eep out of money options and lottery tickets 7
8 M onte Carlo simulations in Excel 9
9 M odel and methodology basics 9
10 T he Black–Scholes–Merton pricing model 11
11 N’(d ) and N’(d ) 1 2
1 2
12 U nderstanding Black–Scholes: an intuitive derivation of
N(d ) and N(d ) 1 2
1 2
i Underlying assumptions 13
ii Estimating the price move 14
iii Plugging in the values 15
iv Receipt of stock and N(d ) 16
1
v Difference between N(d ) and N(d ) 1 7
1 2
1 Delta and Gamma 19
1 T he five Greeks 19
2 I ntroducing Delta 21
i Let’s talk about Delta 21
ii Using Delta: creating the replicating portfolio 26
iii Dissecting Delta 29
3 I ntroducing Gamma 32
i Against strike 3 3
vii
viii Contents
ii A gainst time 34
iii A gainst volatility 42
Appendix 1 – Calculation Examples for At or Near Money Options 44
Appendix 2 – Using Greeks 5 0
Part II Delta Hedging
2 A Simulation Model for Delta Hedging – European Call Options 61
1 Setting the groundwork 62
2 Assumptions 62
3 Simulating the stock price 64
4 Calculating Delta 65
5 Calculating total borrowing 66
6 Putting it all together 69
7 Next steps, and questions 70
3 Delta Hedging European Put Options 71
1 Tweaking the original Monte Carlo simulation model 72
2 Assumptions 73
3 Simulating the underlying 74
4 Calculating the amount lent 76
5 Putting the rest of the sheet together 77
4 Calculating Cash P&L for a Call Option 79
1 Dissecting the P&L model 80
i Interest paid and principal borrowed for the hedge 82
ii Calculating the trading loss on account of selling low 8 4
iii Putting it all together 85
2 The vexing question of trading gain (loss) 88
3 Next steps, and questions 89
5 Calculating Cash P&L for a Put Option 91
1 Dissecting the P&L model 91
i Interest paid and principal borrowed for the hedge 92
ii Calculating the trading gain/loss 93
iii Putting it all together 95
Part III Building Surfaces in Excel
6 Understanding Volatility 1 01
1 The many flavours of volatility 101
2 E nter volatility surface 103
3 The difference between implied and local volatilities 1 05
i Implied volatilities 105
ii L ocal volatilities 106
Contents ix
7 B uilding Volatility Surfaces 109
1 Creating the implied volatility dataset 1 09
2 Building local volatility surfaces in Excel 1 13
3 Next steps, and questions 124
8 F orward Implied Volatilities 125
1 Comparing local, implied and forward volatilities 1 28
Part IV Hedging Higher-Order Greeks
9 V ega, Volga and Vanna 133
1 Vega 1 33
2 Vanna 1 34
3 Volga 1 35
4 Plotting Vega and Gamma 1 36
i Against strike 136
ii Against time 137
5 Shadow Gamma – including the impact of volatility
changes 1 38
6 Vega, Gamma, Vanna and Volga surfaces 1 42
7 Next steps, and questions 1 44
10 H edging Higher-Order Greeks 146
1 Hedging Gamma and Vega – framework 1 48
i Hedging higher-order Greeks for a single short position 149
11 Reviewing the Solver Solution 158
1 Hedging Gamma and Vega for a book of options 1 62
2 Hedging portfolio Vega and Gamma using Solver 1 66
i Constraints review 1 68
ii Solver solution – first pass 1 69
3 Minimizing hedge portfolio cost 1 71
4 Optimizing Delta 1 75
5 Next Steps, and questions 1 78
Part V Applications
12 R ebalancing, Implied Vol and Rho 181
1 Assumptions and securities 1 81
2 Rebalancing frequency and efficiency of the hedge:
implications for profitability? 1 82
i The Gamma correction 1 85
3 Volatility and profitability: the question of implied volatility 186
i Implied volatility and P&L – four scenarios to set
things right 1 88