On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance
Event-driven uncertainties such as corporate defaults, operational failures or central bank announcements are important elements in the modelling of financial quantities. Therefore, stochastic differential equations (SDEs) of jump-diffusion 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 predictor-corrector 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.
|Date of creation:||01 Jul 2006|
|Date of revision:|
|Publication status:||Published as: Bruti-Liberati, N. and Platen, E, 2012, "On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance", In: Topics in Numerical Methods for Finance, Volume 19 of the series Springer Proceedings in Mathematics and Statistics, 1-13.|
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