Sebastien Bossu & Philippe Henrotte 
An Introduction to Equity Derivatives 
Theory and Practice

Everything you need to get a grip on the complex world of derivatives

Written by the internationally respected academic/finance professional author team of Sebastien Bossu and Philipe Henrotte, An Introduction to Equity Derivatives is the fully updated and expanded second edition of the popular Finance and Derivatives. It covers all of the fundamentals of quantitative finance clearly and concisely without going into unnecessary technical detail. Designed for both new practitioners and students, it requires no prior background in finance and features twelve chapters of gradually increasing difficulty, beginning with basic principles of interest rate and discounting, and ending with advanced concepts in derivatives, volatility trading, and exotic products. Each chapter includes numerous illustrations and exercises accompanied by the relevant financial theory. Topics covered include present value, arbitrage pricing, portfolio theory, derivates pricing, delta-hedging, the Black-Scholes model, and more.

* An excellent resource for finance professionals and investors looking to acquire an understanding of financial derivatives theory and practice

* Completely revised and updated with new chapters, including coverage of cutting-edge concepts in volatility trading and exotic products

An accompanying website is available which contains additional resources including powerpoint slides and spreadsheets. Visit www.introeqd.com for details.

Table of Content

Table of Contents iii

Part I. Building Blocks xiii

1. Interest Rate 1

1.Measuring time 1

2. Interest rate 1

3. Discounting 3

4. Problems 4

2. Classical Investment Rules 7

1. Rate of return. Time of return 7

2. Net present value (NPV) 8

3. Internal rate of return (IRR) 9

4. Other investment rules 9

5. Further reading 10

6. Problems 10

3. Fixed markets 13

1. Financial markets 13

2. Bonds 15

3. Yield 16

4. Zero-coupon yield curve. Arbitrage price 18

5. Further reading 21

6. Problems 21

4. Portfolio Theory 25

1. Risk and return of an asset 25

2. Risk and return of a portfolio 27

3. Gains of diversification. Portfolio optimization 30

4. Capital Asset Pricing Model 31

5. Further reading 32

6. Problems 32

Part II. First Steps in Equity Derivatives 35

5. Equity Derivatives 37

1. Introduction 37

2. Forward contracts 38

3. ‘Plain vanilla’ options 42

4. Further reading 47

5. Problems 47

6. The Binomial Model 51

1. One-step binomial model 51

2. Multi-step binomial trees 53

3. Binomial valuation algorithm 54

4. Further reading 56

5. Problems 56

7. The Lognormal Model 59

1. Fair value 59

2. Closed-form formulas for European options 60

3. Monte-Carlo method 61

4. Further reading 62

5. Problems 62

8. Dynamic Hedging 67

1. Hedging option risks 67

2. The P&L of delta-hedged options 69

3. Further reading 72

4. Problems 72

Part III. Advanced Models and Techniques 75

9. Models for Asset Prices in Continuous Time 77

1. Continuously compounded interest rate 77

2. Introduction to models for the behavior of asset prices in continuous time 78

3. Introduction to stochastic processes 79

4. Introduction to stochastic calculus 81

5. Further reading 83

6. Problems 83

10. The Black-Scholes Model 87

1. The Black-Scholes partial differential equation 87

2. The Black-Scholes formulas for European vanilla options 89

3. Volatility 90

4. Further reading 91

5. Problems 81

11. Volatility Trading 95

1. Implied and realized volatilities 95

2. Volatility trading using options 96

3. Volatility trading using variance swaps 97

4. Further reading 100

5. Problems 100

12. Exotic Derivatives 103

1. Single-asset exotics 103

2. Multi-asset exotics 106

3. Beyond Black-Scholes 108

4. Further reading 112

5. Problems 112

Solutions 115

Problem Solutions 117

Appendices 171

A. Probability Review 173

1. States of nature. Random variables. Events 173

2. Probability. Expectation, Variance 174

3. Distribution. Normal distribution 175

4. Independence. Correlation 177

5. Probability formulas 177

6. Further reading 179

B. Calculus Review 181

1. Functions of two variables x and y 181

2. Taylor expansions 181

C. Finance Formulas 183

1. Rate and yields 183

2. Present value. Arbitrage price 183

3. Forward contracts 183

4. Options 184

5. Volatility 185

6. Stochastic processes. Stochastic calculus 185

7. Greeks etc 186

About the author

SÉBASTIEN BOSSU is currently Principal at Ogee
Consulting, a startup company based in New York doing cutting-edge
research on derivatives, investment management and software
development. A former director of Equity Derivatives Structuring
for an investment bank in London, he also worked at J.P. Morgan as
an exotics structurer. He is a graduate from The University of
Chicago, HEC Paris, Columbia University and Université Pierre
et Marie Curie.

PHILIPPE HENROTTE is Head of Financial Theory and
Research at ITO 33, a company which designs sophisticated
derivatives pricing software for hedge funds and financial
institutions; and an Affiliate Professor of Finance at HEC Paris.
An expert in asset pricing and derivatives hedging, he earned his
Ph D from Stanford University after graduating from Ecole
Polytechnique de Paris.