Time-adaptive high-order compact finite difference schemes for option pricing in a family of stochastic volatility models

TL;DR

This paper introduces a high-order, time-adaptive finite difference scheme for option pricing under stochastic volatility models, enhancing accuracy and efficiency in numerical solutions.

Contribution

It develops a novel combination of semi-discrete high-order compact spatial discretisation with adaptive fourth-order multistep time methods for improved option pricing models.

Findings

Achieves higher accuracy in option pricing simulations.

Demonstrates efficiency gains with adaptive time-stepping.

Extends existing methods to fourth-order temporal discretisation.

Abstract

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.