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Achdou Y., Pironneau O. — Computational methods for option pricing
Achdou Y., Pironneau O. — Computational methods for option pricing

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Название: Computational methods for option pricing

Авторы: Achdou Y., Pironneau O.


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: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

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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