Computational Finance Using C and C#

Computational Finance Using C and C#

by: George Levy

Elsevier Trade Monographs, 2008

ISBN: 9780080878072 , 384 Pages

Format: PDF

Windows PC,Mac OSX Apple iPad, Android Tablet PC's Palm OS, PocketPC 2002 und älter, PocketPC 2003 und neuer, Windows Mobile Smartphone, Handys (mit Symbian)

Price: 93,95 EUR

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Computational Finance Using C and C#


 

Cover

Cover

Contents

8

Preface

12

Chapter 1. Overview of financial derivatives

14

Chapter 2. Introduction to stochastic processes

18

2.1 Brownian motion

18

2.2 A Brownian model of asset price movements

22

2.3. Ito's formula (or lemma)

23

2.4 Girsanov's theorem

25

2.5 Ito's lemma for multiasset geometric Brownian motion

26

2.6 Ito product and quotient rules in two dimensions

28

2.7 Ito product in n dimensions

31

2.8 The Brownian bridge

32

2.9 Time-transformed Brownian motion

34

2.10 Ornstein-Uhlenbeck process

37

2.11 The Ornstein-Uhlenbeck bridge

40

2.12 Other useful results

44

2.13 Selected problems

46

Chapter 3. Generation of random variates

50

3.1 Introduction

50

3.2 Pseudo-random and quasi-random sequences

51

3.3 Generation of multivariate distributions: independent variates

54

3.4 Generation of multivariate distributions: correlated variates

60

Chapter 4. European options

72

4.1 Introduction

72

4.2 Pricing derivatives using a martingale measure

72

4.3 Put call parity

73

4.4 Vanilla options and the Black-Scholes model

75

4.5 Barrier options

98

Chapter 5. Single asset American options

110

5.1 Introduction

110

5.2 Approximations for vanilla American options

110

5.3 Lattice methods for vanilla options

127

5.4 Grid methods for vanilla options

148

5.5 Pricing American options using a stochastic lattice

185

Chapter 6. Multiasset options

194

6.1 Introduction

194

6.2 The multiasset Black-Scholes equation

194

6.3 Multidimensional Monte Carlo methods

196

6.4 Introduction to multidimensional lattice methods

198

6.5 Two asset options

203

6.6 Three asset options

214

6.7 Four asset options

218

Chapter 7. Other financial derivatives

222

7.1 Introduction

222

7.2 Interest rate derivatives

222

7.3 Foreign exchange derivatives

241

7.4 Credit derivatives

245

7.5 Equity derivatives

250

Chapter 8. C# portfolio pricing application

258

8.1 Introduction

258

8.2 Storing and retrieving the market data

267

8.3 The PricingUtils class and the Analytics_MathLib

275

8.4 Equity deal classes

280

8.5 FX deal classes

293

Appendix A: The Greeks for vanilla European options

302

A.1 Introduction

302

A.2 Gamma

303

A.3 Delta

304

A.4 Theta

305

A.5 Rho

306

A.6 Vega

307

Appendix B: Barrier option integrals

308

B.1 The down and out call

308

B.2 The up and out call

311

Appendix C: Standard statistical results

316

C.1 The law of large numbers

316

C.2 The central limit theorem

316

C.3 The variance and covariance of random variables

318

C.4 Conditional mean and covariance of normal distributions

323

C.5 Moment generating functions

324

Appendix D: Statistical distribution functions

326

D.1 The normal (Gaussian) distribution

326

D.2 The lognormal distribution

328

D.3 The Student's t distribution

330

D.4 The general error distribution

332

Appendix E: Mathematical reference

334

E.1 Standard integrals

334

E.2 Gamma function

334

E.3 The cumulative normal distribution function

335

E.4 Arithmetic and geometric progressions

336

Appendix F: Black-Scholes finite-difference schemes

338

F.1 The general case

338

F.2 The log transformation and a uniform grid

338

Appendix G: The Brownian bridge: alternative derivation

342

Appendix H: Brownian motion: more results

346

H.1 Some results concerning Brownian motion

346

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

347

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

348

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

348

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

348

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

351

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

351

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

351

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

352

Appendix I: The Feynman-Kac formula

354

Appendix J: Answers to problems

356

J.1 Problem 1

356

J.2 Problem 2

357

J.3 Problem 3

358

J.4 Problem 4

359

J.5 Problem 5

359

J.6 Problem 6

360

J.7 Problem 7

361

J.8 Problem 8

363

J.9 Problem 9

363

J.10 Problem 10

365

J.11 Problem 11

367

References

368

Index

374

Glossary

384