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

摘要

We derive high-order compact finite difference schemes for option pricing instochastic volatility models on non-uniform grids. The schemes are fourth-orderaccurate in space and second-order accurate in time for vanishing correlation.In our numerical study we obtain high-order numerical convergence also fornon-zero correlation and non-smooth payoffs which are typical in optionpricing. In all numerical experiments a comparative standard second-orderdiscretisation is significantly outperformed. We conduct a numerical stabilitystudy which indicates unconditional stability of the scheme.