RBF based some implicit–explicit finite difference schemes for pricing option under extended jump-diffusion model

Abstract

In this manuscript, we presented some efficient and accurate radial basis function-based finite difference (RBF-FD) implicit–explicit (IMEX) numerical techniques for pricing the option when the underlying asset follows the jump-diffusion process with local volatility. For the time semi-discretization, we present three numerical techniques Crank–Nikolson Leap-Frog (CNLF), Crank–Nikolson AdamBashforth (CNAB), and Backward difference formula of order two (BDF2), incorporated with the radial basis function based finite difference (RBF-FD) method. The stabilities of time semi-discretized schemes are also proved. The computational methods developed for the European option are extended for the American option. We amalgamate the RBF-FD implicit–explicit methods with an operator splitting (OS) method for solving the linear complementarity problem (LCP) with variable parameters that determines the price of an American option. In order to demonstrate the effectiveness and precision of the current techniques, numerical data for European and American put options under the Merton and Kou models are presented.