High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids

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.