We propose a time-adaptive, high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation, and combine this with an adaptive time discretisation, extending ideas from [LSRHF02] to fourth-order multistep methods in time.

翻译：我们提出一个适应时间的、高阶紧凑的有限差异计划,用于在随机波动模型大家庭中选择定价。 我们采用半分式高阶紧凑差异法进行空间分化,并结合适应性时间分化,及时将想法从[LSRHF02]扩大到四阶多步法。