Volatility Inference and Return Dependencies in Stochastic Volatility Models

TL;DR

This paper quantifies the information that past stock returns provide about unobserved volatility and future returns within stochastic volatility models using Shannon's mutual information, enhancing understanding of return-volatility dependencies.

Contribution

It introduces a method to measure the mutual information between past returns, volatility, and future returns in stochastic volatility models, providing new insights into return dependencies.

Findings

Quantifies the mutual information between past returns and volatility.

Shows the extent to which past returns inform about future returns.

Provides a framework for analyzing return-volatility dependencies.

Abstract

Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock returns can be inferred from past returns in stochastic volatility models in terms of Shannon's mutual information.