Preface 1
Chapter 1: What is Quantitative Finance? 5
Discipline 1 – finance (financial derivatives) 5
Discipline 2 – mathematics 8
Discipline 3 – informatics (C++ programming) 9
The Bento Box template 10
Summary 12
Chapter 2: Mathematical Models 13
Equity 13
Foreign exchange 17
Interest rates 20
Short rate models 20
Market models 22
Credit 25
Structural models 26
Intensity models 28
Summary 31
Chapter 3: Numerical Methods 33
The Monte Carlo simulation method 34
Algorithm of the MC method 35
Example of the MC method 37
The Binomial Trees method 39
Algorithm of the BT method 39
Example of the BT method 42
Table of Contents
[ ii ]
The Finite Difference method 44
Algorithm of FDM 46
Example of the FD method 48
Summary 50
Chapter 4: Equity Derivatives in C++ 51
Basic example – European Call 51
Advanced example – equity basket 56
Summary 60
Chapter 5: Foreign Exchange Derivatives with C++ 61
Basic example – European FX Call (FX1) 61
Advanced example – FX barrier option (FX2) 68
Summary 73
Chapter 6: Interest Rate Derivatives with C++ 75
Basic example – plain vanilla IRS (IR1) 76
Advanced example – IRS with Cap (IR2) 82
Summary 88
Chapter 7: Credit Derivatives with C++ 89
Basic example – bankruptcy (CR1) 89
Advanced example – CDS (CR2) 94
Summary 100
Appendix A: C++ Numerical Libraries for Option Pricing 101
Numerical recipes 101
Financial numerical recipes 102
The QuantLib project 102
The Boost library 102
The GSL library 103
Appendix B: References 105
Index 107