Convergence analysis of an IMEX scheme for an integro-differential equation with inexact boundary arising in option pricing with stochastic intensity jumps. (English) Zbl 07839865
Summary: In this paper, we are concerned with the convergence rates of an implicit-explicit (IMEX) difference scheme for solving a two-dimensional partial integro-differential equation (PIDE) with an inexact boundary which arises in option pricing with stochastic intensity jumps. First, the IMEX scheme is proposed to solve the two-dimensional PIDE and its inexact boundary governed by a one-dimensional PIDE. Then the second-order convergence rates of the IMEX scheme for the main PIDE are proved for both time and space based on the second-order convergence analysis in the discrete \(H^1\)-norm of the IMEX scheme for the boundary PIDE. Numerical examples are given to illustrate the theoretical results.
MSC:
| 65-XX | Numerical analysis |
| 91-XX | Game theory, economics, finance, and other social and behavioral sciences |
Keywords:
option pricing; stochastic intensity jumps; partial integro-differential equations; inexact boundaries; implicit-explicit finite difference methods; convergence ratesReferences:
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