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

• URL: http://arxiv.org/abs/2507.21337v1
• Date: Mon, 28 Jul 2025 21:06:45 GMT
• Title: On Quantum and Quantum-Inspired Maximum Likelihood Estimation and Filtering of Stochastic Volatility Models
• Authors: Eric Ghysels, Jack Morgan, Hamed Mohammadbagherpoor,
• Abstract summary: We propose two novel approaches to estimating volatility diffusions.<n>One is using Quantum-Inspired Classical Hidden Markov Models (HMM) and the other using Quantum Hidden Markov Models.<n>In both cases we have approximate likelihood functions and filtering algorithms that are easy to compute.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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