American option pricing using generalised stochastic hybrid systems

TL;DR

This paper introduces a new method for pricing American options using generalized stochastic hybrid systems called PDifMPs, which better capture market jumps and fluctuations, leading to improved accuracy and efficiency.

Contribution

The paper develops a novel PDifMP-based approach for American option pricing, integrating discrete jumps with continuous dynamics, and benchmarks it against existing algorithms.

Findings

PDifMP models better reflect market jumps and volatility.

The method improves pricing accuracy over traditional models.

Computational efficiency is enhanced with the new approach.

Abstract

This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard models often rely on constant drift and volatility assumptions, which limits their ability to accurately capture the complex and erratic nature of financial markets. By incorporating PDifMPs, our method accounts for sudden market fluctuations, providing a more realistic model of asset price dynamics. We benchmark our approach with the Longstaff-Schwartz algorithm, both in its original form and modified to include PDifMP asset price trajectories. Numerical simulations demonstrate that our PDifMP-based method not only provides a more accurate reflection of market behaviour but also offers practical advantages in terms of computational efficiency. The results suggest that PDifMPs can significantly improve the predictive accuracy of American options pricing by more closely aligning with the stochastic volatility and jumps observed in real financial markets.