Computational Economics

, Volume 29, Issue 3–4, pp 283–312 | Cite as

Approximation of jump diffusions in finance and economics

Original Paper

Abstract

In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a survey of strong and weak numerical schemes for SDEs with jumps. Strong schemes provide pathwise approximations and therefore can be employed in scenario analysis, filtering or hedge simulation. Weak schemes are appropriate for problems such as derivative pricing or the evaluation of risk measures and expected utilities. Here only an approximation of the probability distribution of the jump-diffusion process is needed. As a framework for applications of these methods in finance and economics we use the benchmark approach. Strong approximation methods are illustrated by scenario simulations. Numerical results on the pricing of options on an index are presented using weak approximation methods.

Keywords

Jump-diffusion processes Discrete time approximation Simulation Strong convergence Weak convergence Benchmark approach Growth Optimal portfolio 

2000 Mathematics subject classification

Primary 60H10 Secondary 65C05 

JEL Classification

G10 G13 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Finance and EconomicsUniversity of Technology SydneyBroadwayAustralia

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