VOLATILITY INFERENCE AND RETURN DEPENDENCIES IN STOCHASTIC VOLATILITY MODELS

Oliver Pfante () and Nils Bertschinger ()
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Oliver Pfante: Systemic Risk Group, Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, Frankfurt, Hesse 60438, Germany
Nils Bertschinger: Systemic Risk Group, Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, Frankfurt, Hesse 60438, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 03, 1-44

Abstract: Stochastic volatility models describe stock returns rt as driven by an unobserved process capturing the random dynamics of volatility vt. The present paper quantifies how much information about volatility vt and future stock returns can be inferred from past returns in stochastic volatility models in terms of Shannon’s mutual information. In particular, we show that across a wide class of stochastic volatility models, including a two-factor model, returns observed on the scale of seconds would be needed to obtain reliable volatility estimates. In addition, we prove that volatility forecasts beyond several weeks are essentially impossible for fundamental information theoretic reasons.

Keywords: Stochastic volatility; Shannon information; geometric probability theory (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500134

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