An IMEX predictor-corrector method for pricing options under regime-switching jump-diffusion models. (English) Zbl 1481.91220
Summary: An efficient second-order method for pricing European and American options under regime-switching jump-diffusion models is presented and analysed for stability and convergence. The implicit-explicit (IMEX) nature of the proposed method avoids the need to invert a full matrix and leads to tridiagonal systems that can be efficiently solved by direct methods. The IMEX predictor-corrector method is coupled with the operator splitting method to solve the linear complementarity problem of the American options. Numerical experiments are performed to demonstrate the stability and second-order convergence of the method.
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
Keywords:
regime-switching jump-diffusion model; option pricing; American options; predictor-corrector method; \(L\)-stableReferences:
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