Computational Finance Using C and C# -  George Levy

Computational Finance Using C and C# (eBook)

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eBook Download: PDF
2008 | 1. Auflage
384 Seiten
Elsevier Science (Verlag)
978-0-08-087807-2 (ISBN)
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78,95 inkl. MwSt
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In Computational Finance Using C and C# George Levy raises computational finance to the next level using the languages of both standard C and C#. The inclusion of both these languages enables readers to match their use of the book to their firm's internal software and code requirements. Levy also provides derivatives pricing information for:
- equity derivates: vanilla options, quantos, generic equity basket options
- interest rate derivatives: FRAs, swaps, quantos
- foreign exchange derivatives: FX forwards, FX options
- credit derivatives: credit default swaps, defaultable bonds, total return swaps.


Computational Finance Using C and C# by George Levy is supported by extensive web resources. Available for purchase on the multi-tier website are e versions of this book and Levy's first book, Computational Finance: Numerical Methods for Pricing Financial Derivatives. Purchasers of the print or e-book can download free software consisting of executable files, configuration files, and results files. With these files the user can run the example portfolio application in Chapter 8 and change the portfolio composition and the attributes of the deals.

In addition, Upgrade Software is available on the website for a small fee, and includes:
. Code to run all the C, C# and Excel examples in the book
. Complete C source code for the Analytics_Mathlib maths library that is used in the book
. C# source code, market data and portfolio files for the portfolio application described in Chapter 8

All the C/C# software can be compiled using either Visual Studio .NET 2005, or the freely available Microsoft Visual C#/C++ 2005 Express Editions.

With this software, the user can open the files and create new deals, new instruments, and change the attributes of the deals by editing the code and recompiling it. This serves as a template that a user can run to customize the deals for their personal, everyday use.

* Complete financial instrument pricing code in standard C and C# available to book buyers on companion website
* Illustrates the use of C# design patterns, including dictionaries, abstract classes, and .NET InteropServices.
Computational Finance Using C and C# raises computational finance to the next level using the languages of both standard C and C#. The inclusion of both these languages enables readers to match their use of the book to their firm's internal software and code requirements. The book also provides derivatives pricing information for equity derivates (vanilla options, quantos, generic equity basket options); interest rate derivatives (FRAs, swaps, quantos); foreign exchange derivatives (FX forwards, FX options); and credit derivatives (credit default swaps, defaultable bonds, total return swaps).This book is organized into 8 chapters, beginning with an overview of financial derivatives followed by an introduction to stochastic processes. The discussion then shifts to generation of random variates; European options; single asset American options; multi-asset options; other financial derivatives; and C# portfolio pricing application. The text is supported by a multi-tier website which enables purchasers of the book to download free software, which includes executable files, configuration files, and results files. With these files the user can run the C# portfolio pricing application and change the portfolio composition and the attributes of the deals.This book will be of interest to financial engineers and analysts as well as numerical analysts in banking, insurance, and corporate finance. Illustrates the use of C# design patterns, including dictionaries, abstract classes, and .NET InteropServices

Cover 
1 
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

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