A finite difference scheme for option pricing in jump diffusion and exponential Levy models

被引:258
作者
Cont, R [1 ]
Voltchkova, E [1 ]
机构
[1] Ecole Polytech, CMAP, F-91128 Palaiseau, France
关键词
parabolic integro-differential equations; finite difference methods; Levy process; jump-diffusion models; option pricing; viscosity solutions;
D O I
10.1137/S0036142903436186
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Levy process or, more generally, a time-inhomogeneous jump-diffusion process. We discuss localization to a finite domain and provide an estimate for the localization error under an integrability condition on the Levy measure. We propose an explicit-implicit finite difference scheme which can be used to price European and barrier options in such models. We study stability and convergence of the scheme proposed and, under additional conditions, provide estimates on the rate of convergence. Numerical tests are performed with smooth and nonsmooth initial conditions.
引用
收藏
页码:1596 / 1626
页数:31
相关论文
共 31 条
[1]   Viscosity solutions of nonlinear integro-differential equations [J].
Alvarez, O ;
Tourin, A .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1996, 13 (03) :293-317
[2]  
Andersen L., 2000, REV DERIV RES, V4, P231, DOI DOI 10.1023/A:1011354913068
[3]  
[Anonymous], 1998, J. Math. Systems Estim. Control
[4]  
[Anonymous], IMA VOL MATH APPL
[5]  
[Anonymous], 1997, ALGEBRA ANALIZ
[6]   IMPLICIT EXPLICIT METHODS FOR TIME-DEPENDENT PARTIAL-DIFFERENTIAL EQUATIONS [J].
ASCHER, UM ;
RUUTH, SJ ;
WETTON, BTR .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (03) :797-823
[7]  
Barles G., 1991, Asymptotic Analysis, V4, P271
[8]   On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations [J].
Barles, G ;
Jakobsen, ER .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2002, 36 (01) :33-54
[9]  
Barles G., 1997, Stochastics Stochastics Rep., V60, P57, DOI 10.1080/17442509708834099
[10]  
Barndorff-Nielsen O.E., 1997, Finance and Stochastics, V2, P41, DOI DOI 10.1007/S007800050032