Table Of Contents:
Preface xi

Part I Using Numerical Software Components within Microsoft Windows 1(74)

Introduction 3(3)

Dynamic Link Libraries (DLLs) 6(22)

Visual Basic and Excel VBA 6(10)

VB.NET 16(5)

C# 21(7)

ActiveX and COM 28(10)

Introduction 28(2)

The COM interface IDispatch 30(1)

Type libraries 31(1)

Using IDispatch 31(2)

ActiveX controls and the Internet 33(1)

Using ActiveX components on a Web page 34(4)

A financial derivative pricing example 38(6)

Interactive user-interface 38(1)

Language user-interface 38(3)

Use within Delphi 41(3)

ActiveX components and numerical optimization 44(10)

Ray tracing example 44(5)

Portfolio allocation example 49(2)

Numerical optimization within Microsoft Excel 51(3)

XML and transformation using XSL 54(10)

Introduction 54(1)

XML 55(2)

XML schema 57(2)

XSL 59(1)

Stock market data example 60(4)

Epilogue 64(11)

Wrapping C with C++ for OO numerics in .NET 64(9)

Final remarks 73(2)

Part II Pricing Assets 75(210)

Introduction 77(10)

An introduction to options and derivatives 77(1)

Brownian motion 78(3)

A Brownian model of asset price movements 81(2)

Ito's lemma in one dimension 83(1)

Ito's lemma in many dimensions 84(3)

Analytic methods and single asset European options 87(29)

Introduction 87(1)

Put--call parity 88(2)

Vanilla options and the Black--Scholes model 90(20)

Barrier options 110(6)

Numeric methods and single asset American options 116(105)

Introduction 116(1)

Perpetual options 116(5)

Approximations for vanilla American options 121(16)

Lattice methods for vanilla options 137(22)

Implied lattice methods 159(18)

Grid methods for vanilla options 177(35)

Pricing American options using a stochastic lattice 212(9)

Monte Carlo simulation 221(26)

Introduction 221(1)

Pseudorandom and quasirandom sequences 222(7)

Generation of multivariate distributions: independent variates 229(5)

Generation of multivariate distributions: correlated variates 234(13)

Multiasset European and American options 247(27)

Introduction 247(1)

The multiasset Black--Scholes equation 247(1)

Multidimensional Monte Carlo methods 248(5)

Multidimensional lattice methods 253(4)

Two asset options 257(10)

Three asset options 267(5)

Four asset options 272(2)

Dealing with missing data 274(11)

Introduction 274(1)

Iterative multiple linear regression, MREG 275(3)

The EM algorithm 278(7)

Part III Financial Econometrics 285(90)

Introduction 287(14)

Asset returns 289(2)

Nonsynchronous trading 291(2)

Bid-ask spread 293(1)

Models of volatility 294(2)

Stochastic autoregressive volatility, ARV 296(1)

Generalized hyperbolic Levy motion 297(4)

Garch models 301(10)

Box Jenkins models 301(2)

Gaussian Linear Garch 303(6)

The Igarch model 309(1)

The Garch-M model 309(1)

Regression-Garch and Ar-Garch 310(1)

Nonlinear Garch 311(8)

Agarch-I 313(3)

Agarch-II 316(1)

GJR-Garch 317(2)

Garch conditional probability distributions 319(8)

Gaussian distribution 319(2)

Student's t distribution 321(2)

General error distribution 323(4)

Maximum likelihood parameter estimation 327(9)

The conditional log likelihood 327(1)

The covariance matrix of the parameter estimates 328(4)

Numerical optimization 332(2)

Scaling the data 334(2)

Analytic derivatives of the log likelihood 336(8)

The first derivatives 336(3)

The second derivatives 339(5)

GJR--Garch algorithms 344(9)

Initial estimates and pre-observed values 344(2)

Gaussian distribution 346(4)

Student's t distribution 350(3)

Garch software 353(7)

Expected sofware capabilities 353(1)

Testing Garch software 354(6)

Garch process identification 360(11)

Likelihood ratio test 360(1)

Significance of the estimated parameters 360(1)

The independence of the standardized residuals 360(1)

The distribution of the standardized residuals 361(1)

Modelling the S&P 500 index 362(2)

Excel demonstration 364(4)

Internet Explorer demonstration 368(3)

Multivariate time series 371(4)

Principal component Garch 371(4)

Appendices 375(54)

A Computer code for Part I 377(2)

A.1 The ODL file for the derivative pricing control 377(2)

B Some more option pricing formulae 379(2)

B.1 Binary options 379(1)

B.2 Option to exchange one asset for another 379(1)

B.3 Lookback options 380(1)

C Derivation of the Greeks for vanilla European options 381(5)

C.1 Introduction 381(1)

C.2 Gamma 382(1)

C.3 Delta 383(1)

C.4 Theta 383(1)

C.5 Rho 384(1)

C.6 Vega 385(1)

D Multiasset binomial lattices 386(7)

D.1 Truncated two asset binomial lattice 386(2)

D.2 Recursive two asset binomial lattice 388(3)

D.3 Four asset jump probabilities 391(2)

E Derivation of the conditional mean and covariance for a multivariate normal distribution 393(2)

F Standard statistical results 395(8)

F.1 The law of large numbers 395(1)

F.2 The central limit theorem 395(1)

F.3 The mean and variance of linear functions of random variables 396(1)

F.4 Standard algorithms for the mean and variance 397(2)

F.5 The Hanson and West algorithm for the mean and variance 399(2)

F.6 Jensen's inequality 401(2)

G Derivation of barrier option integrals 403(7)

G.1 The down and out call 403(3)

G.2 The up and out call 406(4)

H Algorithms for an Agarch-I process 410(7)

H.1 Gaussian distribution 410(3)

H.2 Student's t distribution 413(4)

I The general error distribution 417(3)

I.1 Value of λ for variance hi 417(1)

I.2 The kurtosis 417(1)

I.3 The distribution when the shape parameter, a is very large 418(2)

J The Student's t distribution 420(3)

J.1 The kurtosis 420(3)

K Mathematical reference 423(3)

K.1 Standard integrals 423(1)

K.2 Gamma function 423(1)

K.3 The cumulative normal distribution function 424(1)

K.4 Arithmetic and geometric progressions 425(1)

L The stability of the Black-Scholes finite-difference schemes 426(3)

L.1 The general case 426(1)

L.2 The log transformation and a uniform grid 426(3)
Glossary of terms 429(1)
Computing reading list 430(2)
Mathematics and finance references 432(7)
Index 439