A meshless method for Asian style options pricing under the Merton jump-diffusion model

Abstract

In this paper, we consider the partial integro-differential equation arising when a stock follows a Poisson distributed jump process, for the pricing of Asian options. We make use of the meshless radial basis functions with differential quadrature for approximating the spatial derivatives and demonstrate that the algorithm performs effectively well as compared to the commonly employed finite difference approximations. We also employ Strang splitting with the exponential time integration technique to improve temporal efficiency. Throughout the numerical experiments covered in the paper, we show how the proposed scheme can be efficiently employed for the pricing of American style Asian options under both the Black–Scholes and the Merton jump-diffusion models.

Keywords:

• Lévy processes
• jump-diffusion models
• Asian options
• radial basis
• differentia lquadrature
• exponential time integration
• Strang splitting

2010 AMS Subject Classifications:

• 65N35
• 62P05
• 91G20

Disclosure statement

No potential conflict of interest was reported by the authors.