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Approximation of jump diffusions in finance and economics

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  • Nicola Bruti-Liberati

    ()

  • Eckhard Platen

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. Copyright Springer Science+Business Media, LLC 2007

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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 29 (2007)
Issue (Month): 3 (May)
Pages: 283-312

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Handle: RePEc:kap:compec:v:29:y:2007:i:3:p:283-312

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Web page: http://www.springerlink.com/link.asp?id=100248
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Related research

Keywords: Jump-diffusion processes; Discrete time approximation; Simulation; Strong convergence; Weak convergence; Benchmark approach; Growth Optimal portfolio; Primary 60H10; Secondary 65C05; G10; G13;

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  1. Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Jump-Diffusion Processes," Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Guyon, Julien, 2006. "Euler scheme and tempered distributions," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 877-904, June.
  3. Nicola Bruti Liberati & Eckhard Platen, 2004. "On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance," Research Paper Series 114, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  5. Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Kestutis Kubilius & Eckhard Platen, 2001. "Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps," Research Paper Series 54, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
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Cited by:
  1. Dennis Kristensen & Yongseok Shin, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-58, School of Economics and Management, University of Aarhus.

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