On weak predictor-corrector schemes for jump-diffusion processes in finance

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Conference Proceeding
Topics in Numerical Methods for Finance: Proceedings in Mathematics and Statistics, 2012, pp. 1 - 12
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Event-driven uncertainties such as corporate defaults, operational failures, or central bank announcements are important elements in the modeling of financial quantities. Therefore, stochastic differential equations (SDEs) of jumpdiffusion type are often used in finance. We consider in this paper weak discrete time approximations of jump-diffusion SDEs which are appropriate for problems such as derivative pricing and the evaluation of risk measures. We present regular and jump-adapted predictorcorrector schemes with first and second order of weak convergence. The regular schemes are constructed on regular time discretizations that do not include jump times, while the jump-adapted schemes are based on time discretizations that include all jump times. A numerical analysis of the accuracy of these schemes when applied to the jump-diffusion Merton model is provided.
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