Computational Finance: Numerical Methods for Pricing Financial Instruments
Publisher:Butterworth-Heinemann | 2004-01-27 | ISBN:0750657227 | Pages:456 | PDF | 3.4 MB

Review
coding the numerical models in a suitable environment has not, up to this point, been particularly well covered. Until now. - Richard Norgate, Ph.D., Financial Engineering News

One of the Top Ten financial engineering titles published in 2003-2004 - Richard Norgate, Ph.D., Financial Engineering News

Book Description
Computational Finance presents a modern computational approach to mathematical finance within the Windows environment, and contains financial algorithms, mathematical proofs and computer code in C/C++. The author illustrates how numeric components can be developed which allow financial routines to be easily called by the complete range of Windows applications, such as Excel, Borland Delphi, Visual Basic and Visual C++.

These components permit software developers to call mathematical finance functions more easily than in corresponding packages. Although these packages may offer the advantage of interactive interfaces, it is not easy or computationally efficient to call them programmatically as a component of a larger system. The components are therefore well suited to software developers who want to include finance routines into a new application.

Typical readers are expected to have a knowledge of calculus, differential equations, statistics, Microsoft Excel, Visual Basic, C++ and HTML.

A CD-ROM is included which contains: working computer code, demonstration applications and also pdf versions of several research articles.

* Enables reader to incorporate advanced financial modelling techniques in Windows compatible software
* Aids the development of bespoke software solutions covering GARCH volatility modelling, derivative pricing with Partial Differential Equations, VAR, bond and stock options
* Includes CD-ROM with adaptive software

Contents of Computational Finance

PART I: Using Numerical Software Components within Microsoft Windows 1. Introduction 2. Dynamic Link Libraries(DLLs) 2.1 Visual Basic and Excel VBA 2.2 VB.NET 2.3 C# 3. ActiveX and COM 3.1 Introduction 3.2 The COM interface IDispatch 3.3 Type libraries 3.4 Using IDispatch 3.5 ActiveX controls and the Internet 3.6 Using ActiveX components on a Web page 4. A financial derivative pricing example 4.1 Interactive user-interface 4.2 Language user-interface 4.3 Use within Delphi 5. ActiveX components and numerical optimization 5.1 Ray tracing example 5.2 Portfolio allocation example 5.3 Numerical optimization within Microsoft Excel 6. XML and transformation using XSL 6.1 Introduction 6.2 XML 6.3 XML schema 6.4 XSL 6.5 Stock market data example 7. Epilogue 7.1 Wrapping C with C++ for 00 numerics in .NET 7.2 Final remarks PART II: Pricing Assets 8. Introduction 8.1 An introduction to options and derivatives 8.2 Brownian motion 8.3 A Brownian model of asset price movements 8.4 Ito’s lemma in one dimension 8.5 Ito’s lemma in many dimensions 9. Analytic methods and single asset European options 9.1 Introduction 9.2 Put-call parity 9.3 Vanilla options and the Black-Scholes model 9.4 Barrier options 10. Numeric methods and single asset American options 10.1 Introduction 10.2 Perpetual options 10.3 Approximations for vanilla American options 10.4 Lattice methods for vanilla options 10.5 Implied lattice methods 10.6 Grid methods for vanilla options 10.7 Pricing American options using a stochastic lattice 11. Monte Carlo simulation 11.1 Introduction 11.2 Pseudorandom and quasirandom sequences 11.3 Generation of multivariate distributions: independent variates 11.4 Generation of multivariate distributions: correlated variates 12. Multiasset European and American options 12.1 Introduction 12.2 The multiasset Black-Scholes equation 12.4 Multidimensional Monte Carlo methods 12.3 Multidimensional lattice methods 12.5 Two asset options 12.6 Three asset options 12.7 Four asset options 13. Dealing with missing data 13.1 Introduction 13.2 Iterative multiple linear regression 13.3 The EM algorithm PART III: Financial econometrics 14. Introduction 14.1 Asset returns 14.2 Nonsynchronous trading 14.3 Bid-ask spread 14.4 Models of volatility 14.5 Stochastic autoregressive volatility, ARV 14.6 Generalized hyperbolic Levy motion 15. GARCH models 15.1 Box Jenkins models 15.3 Gaussian Linear GARCH models 15.4 The IGARCH model 15.5 The GARCH-M model 15.6 Regression-GARCH and AR-GARCH 16. Nonlinear GARCH 16.1 AGARCH-I 16.2 AGARCH-II 16.3 GJR-GARCH 17. GARCH conditional probability distributions 17.1 Gaussian distribution 17.2 Student’s t-distribution 17.3 General error distribution 18. Maximum likelihood parameter estimation 18.1 The conditional log likelihood 18.2 The covariance matrix of the parameter estimates 18.3 Numerical optimization 18.4 Scaling the data 19. Analytic derivatives of the log likelihood 19.1 The first derivatives 19.2 The second derivatives 20. GJR-GARCH Algorithms 20.1 Initial estimates and pre-observed values 20.2 Gaussian distribution 20.3 Student’s t-distribution 21. Testing GJR-GARCH software 21.1 Expected sofware capabilities 21.2 Testing GARCH software 22. GARCH process identification 22.1 Likelihood ratio test 22.2 Significance of the estimated parameters 22.3 The independence of the standardised residuals 22.4 The distribution of the standardised residuals 22.5 Modelling the S&P 500 index 22.6 Excel demonstration 22.7 Internet Explorer demonstration 23. Multivariate time series 23.1 Principal component GARCH Appendices A. Computer code for Part I A.1 The ODL file for the derivative pricing control B. Some more option pricing formulae B.1 Binary options B.2 Option to exchange one asset for another B.3 Lookback options C . Derivation of the Greeks for vanilla European options C.1 Introduction C.2 Gamma C.3 Delta C.4 Theta C.5 Rho C.6 Vega D. Multiasset binomial lattices D.1 Truncated two asset binomial lattice D.2 Recursive two asset binomail lattice D.3 Four asset jump probabilities E. Derivation of the conditional mean and covariance for a multivariate normal distribution F. Standard statistical results F.1 The law of large numbers F.2 The central limit theorem F.3 The mean and variance of linear functions of random variables F.4 Standard algorithms for the mean and variance F.5 The Hanson and West alogorithm for the mean and variance F.6 Jensen’s inequality G. Derivation of barrier option integrals G.1 The down and out call G.2 The up and out call H. Algorithms for an AGARCH-I process H.1 Gaussian distribution H.2 Student's t-distribution I. The general error distribution I.1 Value of for variance hi I.2 The kurtosis I.3 The distribution when the shape parameter, a, is very large J. The Student's t-distribution J.1 The kurtosis K. Mathematical reference K.1 Standard integrals K.2 Gamma function K.3 The cumulative normal distribution function K.4 Arithmetic and geometric progressions L. The stability of the Black-Scholes finite-di erence schemes L.1 The general case L.2 The log transformation and a uniform grid Glossary of terms Computing reading list Mathematics and finance references Index

About George Levy

George Levy DPhil, University of Oxford Software Developer, Numerical Algorithms Group (NAG) George Levy has a doctorate in mathematical physics from Oxford University. For the last 11 years he has worked at the Numerical Algorithms Group (NAG), developing mathematical and financial software. He has provided technical consultancy to numerous financial institutions, and published articles on numerical modelling, mathematical finance and software engineering. His current research interests include: Windows interfacing, financial time series, option pricing, and numerical modelling on the Internet.

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