Option pricing under a jump-telegraph diffusion model with jumps of random size

ABSTRACT

We present a finite difference method to solve a system of two Partial-Integro Differential Equations which arise from pricing an option under a Jump-Telegraph Diffusion Model for the underlying asset, considering the risk-neutral valuation formula under an equivalent martingale measure. This system is fully discretized using an Implicit–Explicit two-time level scheme and quadrature formulas. The resulting two tridiagonal algebraic linear systems are solved recursively using the Thomas Algorithm. Some numerical results are presented and the numerical order of convergence for the method is estimated. Finally, the robustness of the method is validated against an exact solution obtained for a perturbed problem.

KEYWORDS:

• Telegraph process
• coupled PIDEs
• two-time level scheme

2010 AMS SUBJECT CLASSIFICATIONS:

• 60G51
• 91G60

Acknowledgments

The third author would like to express his sincere appreciation to Calouste Gulbenkian Foundation for granted the scholarship.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

J. Janela  http://orcid.org/0000-0001-6675-5711

J. Guerra  https://orcid.org/0000-0002-5307-7170

Additional information

Funding

The authors were partially supported by the Project CEMAPRE – UID/MULTI/00491/2013 financed by Fundação para a Ciência e a Tecnologia – FCT/MCTES through Portuguese national funds.