IMEX schemes for pricing options under jump–diffusion models

We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump–diffusion process. The schemes include the families of IMEX-midpoint, IMEX-CNAB and IMEX-BDF2 schemes. Each family is defined by a convex combination parameter c∈[0,1]c∈[0,1], which divides the zeroth-order term due to the jumps between the implicit and explicit parts in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restrictions, the IMEX-midpoint family is conditionally stable only for c=0c=0, while the IMEX-CNAB and the IMEX-BDF2 families are conditionally stable for all c∈[0,1]c∈[0,1]. The IMEX-CNAB c=0c=0 scheme produced the smallest error in our numerical experiments.