ADI schemes for valuing European options under the Bates model
Provides numerical methods for pricing options under a stochastic volatility model with jumps, relevant for quantitative finance practitioners.
The paper adapts ADI time discretization schemes to solve PIDEs for European option pricing under the Bates model, demonstrating stability and convergence through numerical experiments.
This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.