High-order ADI scheme for option pricing in stochastic volatility models
arXiv:1512.02529 · doi:10.1016/j.cam.2016.09.040
Abstract
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer's ADI time-stepping method, to obtain an efficient method which is fourth-order accurate in space and second-order accurate in time. Numerical experiments for the European put option pricing problem using Heston's stochastic volatility model confirm the high-order convergence.
18 pages
References in corpus (4)
- High-order compact finite difference scheme for option pricing in stochastic volatility models
- High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions
- High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids
- High-order ADI schemes for convection-diffusion equations with mixed derivative terms