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Approximation of Jump Diffusions in Finance and Economics

Nicola Bruti-Liberati and Eckhard Platen ()

No 176, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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 covergence; weak convergence; benchmark approach; growth optimal portfolio (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2006-05-01
New Economics Papers: this item is included in nep-fin
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Citations: View citations in EconPapers (3) Track citations by RSS feed

Published as: Bruti-Liberati, N. and Platen, E, 2007, "Approximation of Jump Diffusions in Finance and Economics", Computational Economics, 29(3), 283-312.

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