Sparse grid high-order ADI scheme for option pricing in stochastic volatility models

TL;DR

This paper introduces a high-order ADI scheme utilizing sparse grids for efficient option pricing under stochastic volatility models, achieving high accuracy and computational savings.

Contribution

The paper develops a novel sparse grid high-order ADI scheme that improves computational efficiency and accuracy in option pricing models with stochastic volatility.

Findings

Confirmed computational efficiency gains with sparse grid combination technique.

Achieved second-order temporal and fourth-order spatial accuracy.

Validated scheme effectiveness through numerical experiments.

Abstract

We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.