Computational Finance Using C and C#

Cover

Contents

Preface

Chapter 1. Overview of financial derivatives

Chapter 2. Introduction to stochastic processes

2.1 Brownian motion

2.2 A Brownian model of asset price movements

2.3. Ito's formula (or lemma)

2.4 Girsanov's theorem

2.5 Ito's lemma for multiasset geometric Brownian motion

2.6 Ito product and quotient rules in two dimensions

2.7 Ito product in n dimensions

2.8 The Brownian bridge

2.9 Time-transformed Brownian motion

2.10 Ornstein-Uhlenbeck process

2.11 The Ornstein-Uhlenbeck bridge

2.12 Other useful results

2.13 Selected problems

Chapter 3. Generation of random variates

3.1 Introduction

3.2 Pseudo-random and quasi-random sequences

3.3 Generation of multivariate distributions: independent variates

3.4 Generation of multivariate distributions: correlated variates

Chapter 4. European options

4.1 Introduction

4.2 Pricing derivatives using a martingale measure

4.3 Put call parity

4.4 Vanilla options and the Black-Scholes model

4.5 Barrier options

Chapter 5. Single asset American options

5.1 Introduction

5.2 Approximations for vanilla American options

5.3 Lattice methods for vanilla options

5.4 Grid methods for vanilla options

5.5 Pricing American options using a stochastic lattice

Chapter 6. Multiasset options

6.1 Introduction

6.2 The multiasset Black-Scholes equation

6.3 Multidimensional Monte Carlo methods

6.4 Introduction to multidimensional lattice methods

6.5 Two asset options

6.6 Three asset options

6.7 Four asset options

Chapter 7. Other financial derivatives

7.1 Introduction

7.2 Interest rate derivatives

7.3 Foreign exchange derivatives

7.4 Credit derivatives

7.5 Equity derivatives

Chapter 8. C# portfolio pricing application

8.1 Introduction

8.2 Storing and retrieving the market data

8.3 The PricingUtils class and the Analytics_MathLib

8.4 Equity deal classes

8.5 FX deal classes

Appendix A: The Greeks for vanilla European options

A.1 Introduction

A.2 Gamma

A.3 Delta

A.4 Theta

A.5 Rho

A.6 Vega

Appendix B: Barrier option integrals

B.1 The down and out call

B.2 The up and out call

Appendix C: Standard statistical results

C.1 The law of large numbers

C.2 The central limit theorem

C.3 The variance and covariance of random variables

C.4 Conditional mean and covariance of normal distributions

C.5 Moment generating functions

Appendix D: Statistical distribution functions

D.1 The normal (Gaussian) distribution

D.2 The lognormal distribution

D.3 The Student's t distribution

D.4 The general error distribution

Appendix E: Mathematical reference

E.1 Standard integrals

E.2 Gamma function

E.3 The cumulative normal distribution function

E.4 Arithmetic and geometric progressions

Appendix F: Black-Scholes finite-difference schemes

F.1 The general case

F.2 The log transformation and a uniform grid

Appendix G: The Brownian bridge: alternative derivation

Appendix H: Brownian motion: more results

H.1 Some results concerning Brownian motion

H.2 Proof of Eq. (H.1.2)

H.3 Proof of Eq. (H.1.4)

H.4 Proof of Eq. (H.1.5)

H.5 Proof of Eq. (H.1.6)

H.6 Proof of Eq. (H.1.7)

H.7 Proof of Eq. (H.1.8)

H.8 Proof of Eq. (H.1.9)

H.8 Proof of Eq. (H.1.10)

Appendix I: The Feynman-Kac formula

Appendix J: Answers to problems

J.1 Problem 1

J.2 Problem 2

J.3 Problem 3

J.4 Problem 4

J.5 Problem 5

J.6 Problem 6

J.7 Problem 7

J.8 Problem 8

J.9 Problem 9

J.10 Problem 10

J.11 Problem 11

References

Index

Glossary