Numerical study for European option pricing equations with non-levy jumps

ABSTRACT

We numerically study partial integro-differential equations that arise from the pricing of options under jump-diffusion processes using finite difference methods. Two kinds of jump-diffusion models are considered: one with non-Levy type feedback jumps and the other with an information effect in the form of jumps. Computational efficiency was achieved by employing an implicit–explicit time stepping scheme based on the Crank–Nicolson and Adams–Bashforth methods. We present some numerical results of the option pricing models with various non-Levy jump distributions for European call options and explain their implications in the financial market.

KEYWORDS:

• Option pricing
• jump-diffusion processes
• partial integro-differential equations
• finite difference method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60
• 65

Disclosure statement

No potential conflict of interest was reported by the authors.