We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all numerical experiments a comparative standard second-order discretisation is significantly outperformed. We conduct a numerical stability study which indicates unconditional stability of the scheme.
['Bertram Düring', 'Michel Fournié', 'Christof Heuer']
High-Order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Models on Non-Uniform Grids