NUMERICAL SCHEMES FOR OPTION PRICING IN REGIME-SWITCHING JUMP DIFFUSION MODELS

Ionut Florescu (), Ruihua Liu (), Maria Cristina Mariani () and Granville Sewell ()
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Ionut Florescu: Financial Engineering, School of Systems and Enterprises, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030, USA
Ruihua Liu: Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469-2316, USA
Maria Cristina Mariani: Department of Mathematical Sciences, The University of Texas at El Paso, Bell Hall 124, El Paso, TX 79968-0514, USA
Granville Sewell: Department of Mathematical Sciences, The University of Texas at El Paso, Bell Hall 124, El Paso, TX 79968-0514, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 08, 1-25

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.

Keywords: Numerical algorithms; system of partial integro-differential equations; regime-switching jump diffusion; option pricing; implicit and explicit finite element methods (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219024913500465

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