Computational finance using C and C♯ / George Levy.

Series from jacket.

Includes bibliographical references (pages 355-360) and index.

1 Overview of financial derivatives 1 -- 2 Introduction to stochastic processes 5 -- 2.1 Brownian motion 5 -- 2.2 A Brownian model of asset price movements 9 -- 2.3 Ito's formula (or lemma) 10 -- 2.4 Girsanov's theorem 12 -- 2.5 Ito's lemma for multiasset geometric Brownian motion 13 -- 2.6 Ito product and quotient rules in two dimensions 15 -- 2.7 Ito product in n dimensions 18 -- 2.8 The Brownian bridge 19 -- 2.9 Time-transformed Brownian motion 21 -- 2.10 Ornstein-Uhlenbeck process 24 -- 2.11 The Ornstein-Uhlenbeck bridge 27 -- 2.12 Other useful results 31 -- 2.13 Selected problems 33 -- 3 Generation of random variates 37 -- 3.2 Pseudo-random and quasi-random sequences 38 -- 3.3 Generation of multivariate distributions: independent variates 41 -- 3.4 Generation of multivariate distributions: correlated variates 47 -- 4 European options 59 -- 4.2 Pricing derivatives using a martingale measure 59 -- 4.3 Put call parity 60 -- 4.4 Vanilla options and the Black-Scholes model 62 -- 4.5 Barrier options 85 -- 5 Single asset American options 97 -- 5.2 Approximations for vanilla American options 97 -- 5.3 Lattice methods for vanilla options 114 -- 5.4 Grid methods for vanilla options 135 -- 5.5 Pricing American options using a stochastic lattice 172 -- 6 Multiasset options 181 -- 6.2 The multiasset Black-Scholes equation 181 -- 6.3 Multidimensional Monte Carlo methods 183 -- 6.4 Introduction to multidimensional lattice methods 185 -- 6.5 Two asset options 190 -- 6.6 Three asset options 201 -- 6.7 Four asset options 205 -- 7 Other financial derivatives 209 -- 7.2 Interest rate derivatives 209 -- 7.3 Foreign exchange derivatives 228 -- 7.4 Credit derivatives 232 -- 7.5 Equity derivatives 237 -- 8 C♯ portfolio pricing application 245 -- 8.2 Storing and retrieving the market data 254 -- 8.3 The PricingUtils class and the Analytics_MathLib 262 -- 8.4 Equity deal classes 267 -- 8.5 FX deal classes 280 -- Appendix A The Greeks for vanilla European options 289 -- A.2 Gamma 290 -- A.3 Delta 291 -- A.4 Theta 292 -- A.5 Rho 293 -- A.6 Vega 294 -- Appendix B Barrier option integrals 295 -- B.1 The down and out call 295 -- B.2 The up and out call 298 -- Appendix C Standard statistical results 303 -- C.1 The law of large numbers 303 -- C.2 The central limit theorem 303 -- C.3 The variance and covariance of random variables 305 -- C.4 Conditional mean and covariance of normal distributions 310 -- C.5 Moment generating functions 311 -- Appendix D Statistical distribution functions 313 -- D.1 The normal (Gaussian) distribution 313 -- D.2 The lognormal distribution 315 -- D.3 The Student's t distribution 317 -- D.4 The general error distribution 319 -- Appendix E Mathematical reference 321 -- E.1 Standard integrals 321 -- E.2 Gamma function 321 -- E.3 The cumulative normal distribution function 322 -- E.4 Arithmetic and geometric progressions 323 -- Appendix F Black-Scholes finite-difference schemes 325 -- F.1 The general case 325 -- F.2 The log transformation and a uniform grid 325 -- Appendix G The Brownian bridge: alternative derivation 329 -- Appendix H Brownian motion: more results 333 -- H.1 Some results concerning Brownian motion 333 -- H.2 Proof of Eq. (H.1.2) 334 -- H.3 Proof of Eq. (H.1.4) 335 -- H.4 Proof of Eq. (H.1.5) 335 -- H.5 Proof of Eq. (H.1.6) 335 -- H.6 Proof of Eq. (H.1.7) 338 -- H.7 Proof of Eq. (H.1.8) 338 -- H.8 Proof of Eq. (H.1.9) 338 -- H.9 Proof of Eq. (H.1.10) 339 -- Appendix I The Feynman-Kac formula 341 -- Appendix J Answers to problems 343 -- J.1 Problem 1 343 -- J.2 Problem 2 344 -- J.3 Problem 3 345 -- J.4 Problem 4 346 -- J.5 Problem 5 346 -- J.6 Problem 6 347 -- J.7 Problem 7 348 -- J.8 Problem 8 350 -- J.9 Problem 9 350 -- J.10 Problem 10 352 -- J.11 Problem 11 354.

"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."--BOOK JACKET.