Numerical schemes for option pricing in regime-switching jump diffusion models

Ionut Florescu, Ruihua Liu, Maria Cristina Mariani, Granville Sewell

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Abstract

In this paper, we present algorithms to solve a complex system of partial integro-differential equations (PIDE's) of parabolic type. The system is motivated by applications in finance where the solution of the system gives the price of European options in a regime-switching jump diffusion model. The new algorithms are based on theoretical analysis in Florescu et al. (2012) where the proof of convergence of the algorithms is carried out. The problems are also solved using a more traditional approach, where the integral terms (but not the derivative terms) are treated explicitly. Another contribution of this work details a novel type of jump distribution. Empirical evidence suggests that this type of distribution may be more appropriate to model jumps as it makes them more clearly distinguishable from the signal variability.

Original languageEnglish
Article number13500465
JournalInternational Journal of Theoretical and Applied Finance
Volume16
Issue number8
DOIs
StatePublished - Dec 2013

Keywords

  • Numerical algorithms
  • implicit and explicit finite element methods
  • option pricing
  • regime-switching jump diffusion
  • system of partial integro-differential equations

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