Inferring Volatility in the Heston Model and its Relatives -- an Information Theoretical Approach

TL;DR

This paper uses information theory to quantify how much can be learned about unobserved volatility in stochastic models like the Heston model from asset prices, revealing fundamental limits on volatility inference.

Contribution

It provides a novel information-theoretic analysis of volatility inference in the Heston model and related discrete-time models, highlighting inherent uncertainties.

Findings

Significant uncertainty exists in volatility estimates due to fundamental information constraints.

Analytical and numerical methods quantify mutual information between asset prices and volatility.

Results suggest limits on volatility inference even with advanced models.

Abstract

Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $\sigma_t$. Here, we quantify how much information about $\sigma_t$ can be inferred from asset prices $S_t$ in terms of Shannon's mutual information $I(S_t : \sigma_t)$. This motivates a careful numerical and analytical study of information theoretic properties of the Heston model. In addition, we study a general class of discrete time models motivated from a machine learning perspective. In all cases, we find a large uncertainty in volatility estimates for quite fundamental information theoretic reasons.