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Achdou Y., Pironneau O. — Computational methods for option pricing
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Название: Computational methods for option pricing
Авторы: 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.
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Рубрика: Computer science /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2005
Количество страниц: 297
Добавлена в каталог: 20.12.2013
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Предметный указатель
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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