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Achdou Y., Pironneau O. — Computational methods for option pricing
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Название: Computational methods for option pricingАвторы: Achdou Y., Pironneau O. Аннотация: Here is a book for anyone who would like to become better acquainted with the modern tools of numerical analysis for several significant computational problems arising in finance. The authors review some important aspects of finance modeling involving partial differential equations and focus on numerical algorithms for the fast and accurate pricing of financial derivatives and for the calibration of parameters.
Option pricing has become a technical topic that requires sophisticated numerical methods for robust and fast numerical solutions. This book explores the best numerical algorithms and discusses them in depth, from their mathematical analysis up to their implementation in C++ with efficient numerical libraries. Much of this information is not available elsewhere. In particular, this is one of the few books that gives detailed coverage of the following topics:
Mathematical results and efficient algorithms for pricing American options. Modern algorithms with adaptive mesh refinement for European and American options. Regularity and error estimates are derived and give strong support to the mesh adaptivity, an essential tool for speeding up the numerical implementations. Calibration of volatility with European and American options. The use of automatic differentiation of computer codes for computing greeks.
This is a book for postgraduate students, professional scientists in the field of finance, researchers, numerical code developers, and those well versed in numerical analysis desiring to learn about numerical and mathematical finance.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2005Количество страниц: 297Добавлена в каталог: 20.12.2013Операции: Положить на полку |
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A posteriori error estimates 96 a posteriori error indicators 156 A priori error estimates 95 Adaptive mesh refinement 151 Adaptive method for American options 208 Adaptive method for basket options 172 Adaptive method for European options 165 Adjoint state 248 269 Algorithm, Brennan and Schwartz 201 Algorithm, front tracking 201 Algorithm, projected SOR 199 Algorithm, SOR 199 Algorithms for the American puts 198 American options 185 American options, calibration with 263 Antithetic variate 13 Arbitrage 2 Armijo's Rule 231 Asian option 85 Automatic differentiation 222 Barrier options 43 Barycentric coordinates 101 Basket options 46 83 126 172 Binomial option pricing 17 Binomial tree 17 Black — Scholes formula 6 Brownian motion 3 Calibration 4 Calibration with American options 263 Calibration with European options 243 Calibration, of jump diffusion models 243 Calibration, stochastic control approach 257 Central limit theorem 11 CFL condition 63 CMGY process 45 117 Compressed row storage 137 Consistency of the Crank — Nicolson scheme 70 Consistency of the Euler explicit scheme 61 Consistency of the Euler implicit scheme 67 Consistency, definition 60 Control variate 13 Convergence of the Euler explicit scheme 64 Convergence of the Euler implicit scheme 69 Convergence of the Euler implicit scheme in the primitive variables 80 Convergence of the finite element method 95 Convergence of the finite element method for the American put 195 Convergence, definition 61 Convexity of the European put's price 38 Crank — Nicolson scheme 69 Diagonal dominant matrix 72 199 Dividends 27 Dividends, discretely paid dividends 27 Drift 3 Dupire's equation 40 Dupire's equation for calibration 243 entropy 257 Euler explicit scheme 58 Euler implicit scheme 66 Exercise boundary 189 Exercise boundary, discrete 198 Filtration 2 Filtration, natural 2 Finite difference scheme 57 Finite difference scheme for Asian options 85 Finite difference scheme for basket options 83 Finite difference scheme for European options 81 Finite elements for American options 192 Finite elements for basket options 126 Finite elements for European options 107 Finite elements for options on Levy driven assets 114 Finite elements for stochastic volatility models 133 Finite elements with variable meshes 155 Finite elements, adaptive, for American options 208 Finite elements, adaptive, for basket options 172 Finite elements, adaptive, for European options 165 Finite elements, adaptivity 151 Finite elements, stabilization 103 Free boundary for the American put 189 Free boundary in the discrete problem for the American put 198 Garding's inequality 32—35 77 153 187 193 194 196 198 GNU Scientific library 7 Gradient method 230 Greeks 223 Greeks delta 223 Greeks gamma 223 Greeks kappa 223 Greeks rho 223 Greeks time-decay 223 Hamilton — Jacobi — Bellman equation 258 Hedging 4 High dimensions 142 Infinitesimal generator 24 Interest rate 3 Ito's formula 23 24 51 260 Ito's formula, multidimensional 46 Ito's formula, two-dimensional 49 50 Jump diffusion 44 Lagrange finite elements 99 Least squares inverse problem 243 Levy driven assets 44 114 Levy process 44 Line search rules 232 Local volatility 27 104 209 localization 39 Logarithmic prices 26 M-matrix 72 267 268 Martingale 2 Mass lumping 102 106 Mass matrix 100 Matrix assembly in the finite element method 128 maturity 1 Maximum principle 35 190 Maximum principle, consequences 37 Maximum principle, discrete 72 267 268 monte-carlo 8 Nodal basis 101 Optimality conditions for calibration with American options 268 Optimality conditions for calibration with Dupire's equation 249 Optimization problem ill-posed 229 Optimization problem ill-posed, stiff 230 Optimization problem ill-posed, unstable 229 Option, American 15 Option, Asian 16 Option, barrier 5 10 Option, cash or nothing 5 Option, European call 1 Option, European put 5 Option, exercise the 1 Option, lookback 17 Option, on a basket 6 Option, vanilla 1 Payoff 5 Penalized problem for the American put 188 Penalized problem for the American put, discrete 265 Primitive variables (Black — Scholes equation in the) 76 Put-call parity 5 38 Random variable, numerical 8 Random variable, with the GSL 12 Security 1 Shape functions 102 Smile 228 Sparse tensor product spaces 142 Spot price 1 Stability by the energy method 79 Stability condition 63 Stability in the finite element method 156 Stability of the Crank — Nicolson scheme 70 Stability of the Euler explicit scheme 61 Stability of the Euler implicit scheme 68 Stability of the Euler scheme for the American puts 194 Stability, definition 60 Steepest descent 231 Step size 230 Stiffness matrix 100 Stochastic control 257 Stochastic volatility 48 133 Stopping time 2 Strike 1 Super-replication principle 38 Transparent boundary condition 110 Triangulation 95 Tychonoff functional 245 Tychonoff regularization 229 Underlying asset 1 Upwinding 71 85 Variance Gamma process 45 Variance reduction 12 Variational inequality 186 Volatility 3 Volatility, historical 228 Volatility, implied 228 Volatility, local 4 228 Wavelets 142 Weak (or variational) formulation 31 96 186
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