DMCA
Pricing Options in Jump-Diffusion Models: An Extrapolation Approach (2008)
| Citations: | 17 - 3 self |
BibTeX
@MISC{Feng08pricingoptions,
author = {Liming Feng and Vadim Linetsky},
title = { Pricing Options in Jump-Diffusion Models: An Extrapolation Approach},
year = {2008}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integrodifferential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) term is treated explicitly. In particular, the popular IMEX Euler scheme is first-order accurate in time. Second-order accuracy in time can be achieved by using the IMEX midpoint scheme. In contrast to the above approaches, we propose a new high-order time discretization scheme for the PIDE based on the extrapolation approach to the solution of ODEs that also treats the diffusion term implicitly and the jump term explicitly. The scheme is simple to implement, can be added to any PIDE solver based on the IMEX Euler scheme, and is remarkably fast and accurate. We demonstrate our approach on the examples of Merton’s and Kou’s jump-diffusion models, the diffusion-extended variance gamma model, as well as the two-dimensional Duffie-Pan-Singleton model with correlated and contemporaneous jumps in the stock price and its volatility. By way of example, pricing a one-year double-barrier option in Kou’s jump-diffusion model, our scheme attains accuracy of 10−5 in 72 time steps (in 0.05 seconds). In contrast, it takes the first-order IMEX Euler scheme more than 1.3 million time steps (in 873 seconds) and the second-order IMEX midpoint scheme 768 time steps (in 0.49 seconds) to attain the same accuracy. Our scheme is also well suited for Bermudan options. Combining simplicity of implementation and remarkable gains in computational efficiency, we expect this method to be very attractive
Keyphrases
jump-diffusion model extrapolation approach time step one-year double-barrier option two-dimensional duffie-pan-singleton model second-order accuracy contemporaneous jump popular imex euler scheme new high-order time discretization scheme imex euler scheme pide solver jump term diffusion-extended variance gamma model new computational method second-order imex midpoint scheme bermudan option stock price time discretization scheme option value function computational efficiency first-order imex euler scheme partial integrodifferential equation diffusion term first-order accurate barrier option remarkable gain imex midpoint scheme
