An Introduction to Equity Derivatives Theory and Practice

by Bossu, Sebastien; Henrotte, Philippe

• ISBN13: 9781119961857
• ISBN10: 1119961858
• Edition: 2nd
• Format: Hardcover
• Copyright: 2012-05-14
• Publisher: Wiley

Summary

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 accompanying website features supplementary material for readers 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 New foreword by Emmanuel Derman, one of the world's most acclaimed research scientists in quantitative finance

Author Biography

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 PhD from Stanford University after graduating from Ecole Polytechnique de Paris.

Table of Contents

Foreword xi

Preface xiii

Addendum: A Path to Economic Renaissance xv

PART I BUILDING BLOCKS

1 Interest Rate 3

1-1 Measuring Time 3

1-2 Interest Rate 4

1-2.1 Gross Interest Rate 4

1-2.2 Compounding. Compound Interest Rate 5

1-2.3 Conversion Formula 6

1-2.4 Annualization 6

1-3 Discounting 7

1-3.1 Present Value 7

1-3.2 Discount Rate and Required Return 8

1-4 Problems 8

2 Classical Investment Rules 11

2-1 Rate of Return. Time of Return 11

2-1.1 Gross Rate of Return (ROR) 11

2-1.2 Time of Return (TOR) 11

2-2 Net Present Value (NPV) 12

2-3 Internal Rate of Return (IRR) 13

2-4 Other Investment Rules 14

2-5 Further Reading 15

2-6 Problems 15

3 Fixed Income 19

3-1 Financial Markets 19

3-1.1 Securities and Portfolios 19

3-1.2 Value and Price 19

3-1.3 Financial Markets and Short-selling 20

3-1.4 Arbitrage 21

3-1.5 Price of a Portfolio 22

3-2 Bonds 23

3-2.1 Treasury Bonds 23

3-2.2 Zero-Coupon Bonds 23

3-2.3 Bond Markets 23

3-3 Yield 24

3-3.1 Yield to Maturity 24

3-3.2 Yield Curve 24

3-3.3 Approximate Valuation 26

3-4 Zero-Coupon Yield Curve. Arbitrage Price 27

3-4.1 Zero-Coupon Rate Curve 27

3-4.2 Arbitrage Price of a Bond 28

3-4.3 Zero-Coupon Rate Calculation by Inference: the ‘Bootstrapping’ Method 29

3-5 Further Reading 30

3-6 Problems 30

4 Portfolio Theory 35

4-1 Risk and Return of an Asset 35

4-1.1 Average Return and Volatility 35

4-1.2 Risk-free Asset. Sharpe Ratio 37

4-2 Risk and Return of a Portfolio 38

4-2.1 Portfolio Valuation 38

4-2.2 Return of a Portfolio 38

4-2.3 Volatility of a Portfolio 39

4-3 Gains of Diversification. Portfolio Optimization 41

4-4 Capital Asset Pricing Model 43

4-5 Further Reading 44

4-6 Problems 44

PART II FIRST STEPS IN EQUITY DERIVATIVES

5 Equity Derivatives 49

5-1 Introduction 49

5-2 Forward Contracts 50

5-2.1 Payoff 51

5-2.2 Arbitrage Price 51

5-2.3 Forward Price 53

5-2.4 Impact of Dividends 53

5-2.4.1 Single Cash Dividend 54

5-2.4.2 Single Proportional Dividend 55

5-3 ‘Plain Vanilla’ Options 55

5-3.1 Payoff 56

5-3.2 Option Value 57

5-3.3 Put-Call Parity 57

5-3.4 Option Strategies 58

5-3.4.1 Leverage 58

5-3.4.2 Covered Call 59

5-3.4.3 Straddle 60

5-3.4.4 Butterfly 61

5-4 Further Reading 61

5-5 Problems 61

6 The Binomial Model 65

6-1 One-Step Binomial Model 65

6-1.1 An Example 65

6-1.2 General Formulas 67

6-2 Multi-Step Binomial Trees 67

6-3 Binomial Valuation Algorithm 69

6-4 Further Reading 70

6-5 Problems 70

7 The Lognormal Model 75

7-1 Fair Value 75

7-1.1 Probability Distribution of ST 75

7-1.2 Discount Rate 76

7-2 Closed-Form Formulas for European Options 76

7-3 Monte-Carlo Method 78

7-4 Further Reading 78

7-5 Problems 78

8 Dynamic Hedging 83

8-1 Hedging Option Risks 83

8-1.1 Delta-hedging 84

8-1.2 Other Risk Parameters: the ‘Greeks’ 85

8-1.3 Hedging the Greeks 86

8-2 The P&L of Delta-hedged Options 86

8-2.1 Gamma 86

8-2.2 Theta 87

8-2.3 Option Trading P&L Proxy 88

8-3 Further Reading 89

8-4 Problems 89

PART III ADVANCED MODELS AND TECHNIQUES

9 Models for Asset Prices in Continuous Time 95

9-1 Continuously Compounded Interest Rate 95

9-1.1 Fractional Interest Rate 95

9-1.2 Continuous Interest Rate 96

9-2 Introduction to Models for the Behavior of Asset Prices in Continuous Time 96

9-3 Introduction to Stochastic Processes 97

9-3.1 Standard Brownian Motion 98

9-3.2 Generalized Brownian Motion 99

9-3.3 Geometric Brownian Motion 100

9-4 Introduction to Stochastic Calculus 101

9-4.1 Ito Process 101

9-4.2 The Ito-Doeblin Theorem 101

9-4.3 Heuristic Proof of the Ito-Doeblin Theorem 102

9-5 Further Reading 103

9-6 Problems 103

10 The Black-Scholes Model 109

10-1 The Black-Scholes Partial Differential Equation 109

10-1.1 Ito-Doeblin Theorem for the Derivative’s Value 110

10-1.2 Riskless Hedged Portfolio 111

10-1.3 Arbitrage Argument 111

10-1.4 Partial Differential Equation 111

10-1.5 Continuous Delta-hedging 112

10-2 The Black-Scholes Formulas for European Vanilla Options 112

10-3 Volatility 113

10-3.1 Historical Volatility 113

10-3.2 Implied Volatility 114

10-4 Further Reading 114

10-5 Problems 114

11 Volatility Trading 117

11-1 Implied and Realized Volatilities 117

11-1.1 Realized Volatility 117

11-1.2 Implied Volatility 117

11-2 Volatility Trading Using Options 118

11-3 Volatility Trading Using Variance Swaps 119

11-3.1 Variance Swap Payoff 120

11-3.2 Variance Swap Market 120

11-3.3 Variance Swap Hedging and Pricing 120

11-4 Further Reading 123

11-5 Problems 123

12 Exotic Derivatives 127

12-1 Single-Asset Exotics 127

12-1.1 Digital Options 127

12-1.2 Asian Options 127

12-1.3 Barrier Options 128

12-1.4 Lookback Options 129

12-1.5 Forward Start Options 129

12-1.6 Cliquet Options 130

12-1.7 Structured Products 130

12-2 Multi-Asset Exotics 131

12-2.1 Spread Options 131

12-2.2 Basket Options 132

12-2.3 Worst-of and Best-of Options 132

12-2.4 Quanto Options 133

12-2.5 Structured Products 133

12-2.6 Dispersion and Correlation Trading 134

12-3 Beyond Black-Scholes 134

12-3.1 Black-Scholes on Multiple Assets 134

12-3.2 Fitting the Smile 135

12-3.2.1 Stochastic Volatility 135

12-3.2.2 Jumps 135

12-3.2.3 Local Volatility 136

12-3.3 Discrete Hedging and Transaction Costs 137

12-3.3.1 Discrete Hedging 137

12-3.3.2 Transaction Costs 137

12-3.4 Correlation Modeling 138

12-4 Further Reading 139

12-5 Problems 139

SOLUTIONS

Problem Solutions 145

Chapter 1 145

Chapter 2 148

Chapter 3 151

Chapter 4 156

Chapter 5 161

Chapter 6 167

Chapter 7 172

Chapter 8 182

Chapter 9 186

Chapter 10 194

Chapter 11 197

Chapter 12 199

APPENDICES

A Probability Review 205

A-1 States of Nature. Random Variables. Events 205

A-2 Probability. Expectation. Variance 206

A-3 Distribution. Normal Distribution 207

A-4 Independence. Correlation 209

A-5 Probability Formulas 210

A-6 Further Reading 211

B Calculus Review 213

B-1 Functions of Two Variables x and y 213

B-2 Taylor Expansions 214

C Finance Formulas 217

C-1 Rates and Yields 217

C-2 Present Value. Arbitrage Price 217

C-3 Forward Contracts 217

C-4 Options 218

C-5 Volatility 219

C-6 Stochastic Processes. Stochastic Calculus 220

C-7 Greeks etc. 220

Index 223