Problems and Solutions in Mathematical Finance - Equity Derivatives

Problems and Solutions in Mathematical Finance: Equity Derivatives, Volume 2

TABLE OF CONTENTS

Preface ix

About the Authors xi

1 Basic Equity Derivatives Theory 1

1.1 Introduction 1

1.2 Problems and Solutions 8

1.2.1 Forward and Futures Contracts 8

1.2.2 Options Theory 15

1.2.3 Hedging Strategies 27

2 European Options 63

2.1 Introduction 63

2.2 Problems and Solutions 74

2.2.1 Basic Properties 74

2.2.2 Black–Scholes Model 89

2.2.3 Tree-Based Methods 190

2.2.4 The Greeks 218

3 American Options 267

3.1 Introduction 267

3.2 Problems and Solutions 271

3.2.1 Basic Properties 271

3.2.2 Time-Independent Options 292

3.2.3 Time-Dependent Options 305

4 Barrier Options 351

4.1 Introduction 351

4.2 Problems and Solutions 357

4.2.1 Probabilistic Approach 357

4.2.2 Reflection Principle Approach 386

4.2.3 Further Barrier-Style Options 408

5 Asian Options 439

5.1 Introduction 439

5.2 Problems and Solutions 443

5.2.1 Discrete Sampling 443

5.2.2 Continuous Sampling 480

6 Exotic Options 531

6.1 Introduction 531

6.2 Problems and Solutions 532

6.2.1 Path-Independent Options 532

6.2.2 Path-Dependent Options 586

7 Volatility Models 647

7.1 Introduction 647

7.2 Problems and Solutions 652

7.2.1 Historical and Implied Volatility 652

7.2.2 Local Volatility 685

7.2.3 Stochastic Volatility 710

7.2.4 Volatility Derivatives 769

A Mathematics Formulae 787

B Probability Theory Formulae 797

C Differential Equations Formulae 813

Bibliography 821

Notation 825

Index 829