Description
Book SynopsisDetailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry.
Table of ContentsPreface 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
