On Quantum and Quantum-Inspired Maximum Likelihood Estimation and Filtering of Stochastic Volatility Models

TL;DR

This paper introduces quantum-inspired and quantum hidden Markov models for estimating stochastic volatility in financial models, providing computationally efficient algorithms with tighter bounds than classical methods.

Contribution

It presents novel quantum-inspired and quantum quantum hidden Markov models for stochastic volatility estimation with improved likelihood bounds.

Findings

Quantum HMMs have tighter non-asymptotic bounds than classical models.

Proposed methods are computationally efficient for continuous and discrete time models.

Both approaches outperform classical estimates in accuracy.

Abstract

Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using Quantum-Inspired Classical Hidden Markov Models (HMM) and the other using Quantum Hidden Markov Models. In both cases we have approximate likelihood functions and filtering algorithms that are easy to compute. We show that the non-asymptotic bounds for the quantum HMM are tighter compared to those with classical model estimates.