On Weak Predictor–Corrector Schemes for Jump-Diffusion Processes in Finance [chapter]

Nicola Bruti-Liberati, Eckhard Platen
2012 Topics in Numerical Methods for 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 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
more » ... 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. 200 Mathematics Subject Classification: primary 60H10; secondary 65C05. JEL Classification: G10, G13, C63.
doi:10.1007/978-1-4614-3433-7_1 fatcat:haex7kidwvhwlh5ps5wpoexf4a