Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model

TL;DR

This paper introduces a compact finite difference scheme with Hermite interpolation for efficiently pricing American put options under a regime-switching model, improving accuracy and computational speed.

Contribution

The paper develops a novel fourth-order compact finite difference scheme combined with Hermite interpolation for regime-switching American options pricing, enhancing accuracy and efficiency.

Findings

The scheme accurately prices American put options in regime-switching models.

It outperforms existing methods in computational speed.

Numerical tests confirm the scheme's high accuracy.

Abstract

We consider a system of coupled free boundary problems for pricing American put options with regime-switching. To solve this system, we first employ the logarithmic transformation to map the free boundary for each regime to multi-fixed intervals and then eliminate the first-order derivative in the transformed model by taking derivatives to obtain a system of partial differential equations which we call the asset-delta-gamma-speed equations. As such, the fourth-order compact finite difference scheme can be used for solving this system. The influence of other asset, delta, gamma, and speed options in the present regime is estimated based on Hermite interpolations. Finally, the numerical method is tested with several examples. Our results show that the scheme provides an accurate solution that is fast in computation as compared with other existing numerical methods.