Option pricing under stochastic volatility on a quantum computer

TL;DR

This paper presents quantum algorithms for pricing Asian and barrier options under the Heston stochastic volatility model, demonstrating improved efficiency and reduced hardware requirements for practical quantum advantage in finance.

Contribution

It introduces quantum algorithms combining numerical methods and amplitude estimation for option pricing under stochastic volatility, with a focus on efficiency improvements.

Findings

Weak Euler method matches strong Euler accuracy with less complexity

Eliminating Gaussian state preparation greatly improves efficiency

Resource estimates suggest feasible quantum advantage in financial applications

Abstract

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under typical market conditions. These algorithms are based on combining well-established numerical methods for stochastic differential equations and quantum amplitude estimation technique. In particular, we empirically show that, despite its simplicity, weak Euler method achieves the same level of accuracy as the better-known strong Euler method in this task. Furthermore, by eliminating the expensive procedure of preparing Gaussian states, the quantum algorithm based on weak Euler scheme achieves drastically better efficiency than the one based on strong Euler scheme. Our resource analysis suggests that option pricing under stochastic volatility is a promising application of quantum computers, and that our algorithms render the hardware requirement for reaching practical quantum advantage in financial applications less stringent than prior art.