Generalized finite integration method with Volterra Operator for pricing multi-asset barrier option

Abstract

We investigate in this paper the pricing of European-style barrier options under the Black–Scholes model. Based on the recently developed Generalized Finite Integration Method with Volterra operator (GFIM-V), we apply the Crank–Nicolson scheme to treat the time variable in the governing Black–Scholes equation for pricing multi-asset barrier options. For verification on the accuracy and efficiency of the proposed approach, we construct several numerical experiments for the solutions of multi-asset barrier option prices with various time step sizes and number of spatial nodal points. Comparisons with available exact solution and existing spectral convergent method indicate the advantages of the GFIM-V method in superior accuracy and unconditional stability.