On the Strong Approximation of Jump-Diffusion Processes
AbstractIn financial modelling, filtering and other areas the underlying 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, there is a need for the systematic use of discrete time approximations in corresponding simulations. This paper presents a survey and new results on strong numerical schemes for SDEs of jump-diffusion type. These are relevant for scenario analysis, filtering and hedge simulation in finance. It provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEs driven by Wiener processes and Poisson random measures. The paper covers also derivative free, drift-implicit and jump adapted strong approximations. For the commutative case particular schemes are obtained. Finally, a numerical study on the accuracy of several strong schemes is presented.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 157.
Date of creation: 01 Apr 2005
Date of revision:
jump-diffusion processes; stochastic Taylor expansion; discrete time approximation; simulation; strong convergence;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-05-07 (All new papers)
- NEP-ETS-2005-05-07 (Econometric Time Series)
- NEP-FIN-2005-05-07 (Finance)
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