An introduction to equity derivatives: theory and practice (hardback)

An Introduction to Equity Derivatives is the updated and expanded second edition of the popular Finance and Derivatives: Theory and Practice. Designed for new practitioners, investors and students, the content covers all of the fundamentals of quantitative finance clearly and concisely.

Each chapter of the book includes numerous illustrations and exercises accompanied by the relevant financial theory, covering key topics such as present value, arbitrage pricing, portfolio theory, derivatives pricing, delta-hedging and the Black-Scholes model. Each topic is introduced to the reader in a succinct and consistent style that makes the complex subject matter accessible for those who have no financial background.

This revised and extended edition includes a new foreword written by Professor Emanuel Derman, one of the most acclaimed research scientists in the field of quantitative finance, as well as two new chapters covering cutting-edge concepts, volatility trading and exotic products. The existing chapters have been reworked to include even more accessible content as well as additional examples and illustrations.

The chapters form a sequence of gradual difficulty, separated into three sections. Part one, Building Blocks, covers the fundamental concepts used in quantitative finance, interest rates, the time value of money, bonds and yields, portfolio valuation, risk and return and diversification. Part two, First Steps in Equity Derivatives relies on discrete time concepts and covers forward contracts, options and option strategies, the binomial model, the lognormal model, Monte-Carlo simulations and dynamic hedging. Finally, part three, Advanced Models and Techniques, goes one level higher into continuous time finance and covers models for asset prices, stochastic processes and calculus, the Black-Scholes model, volatility trading, exotic derivatives and advanced models.

Written by the internationally respected author team of Sébastien Bossu and Philippe Henrotte, An Introduction to Equity Derivatives is an excellent resource for finance professionals and investors looking to acquire an understanding of financial derivatives theory and practice.

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...