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Calcolo

, Volume 44, Issue 1, pp 33–57 | Cite as

Implicit–explicit numerical schemes for jump–diffusion processes

  • Maya Briani
  • Roberto Natalini
  • Giovanni Russo
Article

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

Keywords

Stability Region Option Price Stochastic Volatility Integral Term Explicit Numerical Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Maya Briani
    • 1
  • Roberto Natalini
    • 2
  • Giovanni Russo
    • 3
  1. 1.Istituto per le Applicazioni del Calcolo “Mauro Picone” – CNR, 00161 Rome, Italy, & LUISS Guido Carli, 00198 RomeItaly
  2. 2.Istituto per le Applicazioni del Calcolo “Mauro Picone” – CNR, 00161 RomeItaly
  3. 3.Dipartimento di Matematica Pura e Informatica, Università di Catania, 95129 CataniaItaly

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