Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
A Jump-Diffusion Model for Option Pricing
Management Science
A penalty method for American options with jump diffusion processes
Numerische Mathematik
A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion
SIAM Journal on Scientific Computing
On the numerical evaluation of option prices in the variance gamma model
International Journal of Computer Mathematics - RECENT ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
Option Pricing Under a Mixed-Exponential Jump Diffusion Model
Management Science
| Hi-index | 7.29 |
The pricing equations for options on assets that follow jump-diffusion processes contain integrals in addition to the usual differential terms. These integrals usually make such equations expensive to solve numerically. Although Fast Fourier Transform methods can be used to to evaluate the integrals at all mesh points simultaneously, they are costly since the computational region must be extended in order to avoid problems with wrap around. Other numerical difficulties arise when the density function for the jump size is not smooth, as in the Kou double exponential model. We present new solution methods which are based on the fact that even when the problems contain time-dependent parameters the integrals often satisfy easily solved ordinary or parabolic partial differential equations. In particular, we show that by using the operator splitting method proposed by Andersen and Andreasen it is possible to reduce the solution of the pricing equation in the Kou and similar models to a sequence of ordinary differential equations at each time step. We discuss the methods and present results of numerical experiments.