实例介绍
【实例简介】Computational_Finance_Numerical_Methods.pdf
【实例截图】
【核心代码】
Contents Preface xi Part I Using Numerical Software Components within Microsoft Windows 1 1 Introduction 3 2 Dynamic Link Libraries(DLLs) 6 2.1 Visual Basic and Excel VBA 6 2.2 VB.NET 16 2.3 C# 21 3 ActiveX and COM 28 3.1 Introduction 28 3.2 The COM interface IDispatch 30 3.3 Type libraries 31 3.4 Using IDispatch 31 3.5 ActiveX controls and the Internet 33 3.6 Using ActiveX components on a Web page 34 4 A financial derivative pricing example 38 4.1 Interactive user-interface 38 4.2 Language user-interface 38 4.3 Use within Delphi 41 5 ActiveX componentsand numerical optimization 44 5.1 Ray tracing example 44 5.2 Portfolio allocation example 49 5.3 Numerical optimization within Microsoft Excel 51 6 XML and transformation using XSL 54 6.1 Introduction 54 6.2 XML 55 //SYS21///INTEGRAS/ELS/PAGINATION/ELSEVIER UK/CMF/3B2/FINALS_21-11-03/PRELIMS.3D – 8 – [1–14/14] 21.11.2003 2:55PM 6.3 XML schema 57 6.4 XSL 59 6.5 Stock market data example 60 7 Epilogue 64 7.1 Wrapping C with Cþþ for OO numerics in .NET 64 7.2 Final remarks 73 Part II Pricing Assets 75 8 Introduction 77 8.1 An introduction to options and derivatives 77 8.2 Brownian motion 78 8.3 A Brownian model of asset price movements 81 8.4 Ito’s lemma in one dimension 83 8.5 Ito’s lemma in many dimensions 84 9 Analytic methods and single asset European options 87 9.1 Introduction 87 9.2 Put–call parity 88 9.3 Vanilla options and the Black–Scholes model 90 9.4 Barrier options 110 10 Numeric methods and single asset American options 116 10.1 Introduction 116 10.2 Perpetual options 116 10.3 Approximations for vanilla American options 121 10.4 Lattice methods for vanilla options 137 10.5 Implied lattice methods 159 10.6 Grid methods for vanilla options 177 10.7 Pricing American options using a stochastic lattice 212 11 Monte Carlo simulation 221 11.1 Introduction 221 11.2 Pseudorandomand quasirandomsequences 222 11.3 Generation of multivariate distributions: independent variates 229 11.4 Generation of multivariate distributions: correlated variates 234 12 Multiasset European and American options 247 12.1 Introduction 247 12.2 The multiasset Black–Scholes equation 247 12.3 Multidimensional Monte Carlo methods 248 12.4 Multidimensional lattice methods 253 12.5 Two asset options 257 viii Contents //SYS21///INTEGRAS/ELS/PAGINATION/ELSEVIER UK/CMF/3B2/FINALS_21-11-03/PRELIMS.3D – 9 – [1–14/14] 21.11.2003 2:55PM 12.6 Three asset options 267 12.7 Four asset options 272 13 Dealing with missing data 274 13.1 Introduction 274 13.2 Iterative multiple linear regression, MREG 275 13.3 The EM algorithm278 Part III Financial Econometrics285 14 Introduction 287 14.1 Asset returns 289 14.2 Nonsynchronous trading 291 14.3 Bid-ask spread 293 14.4 Models of volatility 294 14.5 Stochastic autoregressive volatility, ARV 296 14.6 Generalized hyperbolic Levy motion 297 15 GARCH models301 15.1 Box Jenkins models 301 15.2 Gaussian Linear GARCH 303 15.3 The IGARCH model 309 15.4 The GARCH-M model 309 15.5 Regression-GARCH and AR-GARCH 310 16 Nonlinear GARCH 311 16.1 AGARCH-I 313 16.2 AGARCH-II 316 16.3 GJR–GARCH 317 17 GARCH conditional probability distributions 319 17.1 Gaussian distribution 319 17.2 Student’s t distribution 321 17.3 General error distribution 323 18 Maximum likelihood parameter estimation 327 18.1 The conditional log likelihood 327 18.2 The covariance matrix of the parameter estimates 328 18.3 Numerical optimization 332 18.4 Scaling the data 334 19 Analytic derivativesof the log likelihood 336 19.1 The first derivatives 336 19.2 The second derivatives 339 Contents ix //SYS21///INTEGRAS/ELS/PAGINATION/ELSEVIER UK/CMF/3B2/FINALS_21-11-03/PRELIMS.3D – 10 – [1–14/14] 21.11.2003 2:55PM 20 GJR–GARCH algorithms344 20.1 Initial estimates and pre-observed values 344 20.2 Gaussian distribution 346 20.3 Student’s t distribution 350 21 GARCH software 353 21.1 Expected sofware capabilities 353 21.2 Testing GARCH software 354 22 GARCH process identification 360 22.1 Likelihood ratio test 360 22.2 Significance of the estimated parameters 360 22.3 The independence of the standardized residuals 360 22.4 The distribution of the standardized residuals 361 22.5 Modelling the S&P 500 index 362 22.6 Excel demonstration 364 22.7 Internet Explorer demonstration 368 23 Multivariate time series 371 23.1 Principal component GARCH 371 Appendices375 A Computer code for Part I 377 A.1 The ODL file for the derivative pricing control 377 B Some more option pricing formulae 379 B.1 Binary options 379 B.2 Option to exchange one asset for another 379 B.3 Lookback options 380 C Derivation of the Greeksfor vanilla European options 381 C.1 Introduction 381 C.2 Gamma 382 C.3 Delta 383 C.4 Theta 383 C.5 Rho 384 C.6 Vega 385 D Multiasset binomial lattices 386 D.1 Truncated two asset binomial lattice 386 D.2 Recursive two asset binomial lattice 388 D.3 Four asset jump probabilities 391 x Contents //SYS21///INTEGRAS/ELS/PAGINATION/ELSEVIER UK/CMF/3B2/FINALS_21-11-03/PRELIMS.3D – 11 – [1–14/14] 21.11.2003 2:55PM E Derivation of the conditional mean and covariance for a multivariate normal distribution 393 F Standard statistical results 395 F.1 The law of large numbers 395 F.2 The central limit theorem 395 F.3 The mean and variance of linear functions of random variables 396 F.4 Standard algorithms for the mean and variance 397 F.5 The Hanson and West algorithmfor the mean and variance 399 F.6 Jensen’s inequality 401 G Derivation of barrier option integrals403 G.1 The down and out call 403 G.2 The up and out call 406 H Algorithmsfor an AGARCH-I process 410 H.1 Gaussian distribution 410 H.2 Student’s t distribution 413 I The general error distribution 417 I.1 Value of for variance hi 417 I.2 The kurtosis 417 I.3 The distribution when the shape parameter, a is very large 418 J The Student’s t distribution 420 J.1 The kurtosis 420 K Mathematical reference 423 K.1 Standard integrals 423 K.2 Gamma function 423 K.3 The cumulative normal distribution function 424 K.4 Arithmetic and geometric progressions 425 L The stability of the Black–Scholes finite-difference schemes 426 L.1 The general case 426 L.2 The log transformation and a uniform grid 426 Glossary of terms 429 Computing reading list 430 Mathematics and finance references 432 Index 439
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