Abstract
We study the numerical approximation of solutions for parabolic integro-differential equations (PIDE). Similar models arise in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference schemes are not practically feasible. Here we propose using implicit-explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher-order accuracy schemes under weak stability time-step restrictions. Numerical tests are presented to show the computational efficiency of the approximation.
Mathematics Subject Classification (1991): Primary: 65M12; Secondary: 35K55, 49L25
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Briani, M., Natalini, R. & Russo, G. Implicit–explicit numerical schemes for jump–diffusion processes. Calcolo 44, 33–57 (2007). https://doi.org/10.1007/s10092-007-0128-x
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DOI: https://doi.org/10.1007/s10092-007-0128-x