Identifying the volatility risk price through the leverage effect

Xu Cheng, Eric Renault and Paul Sangrey

Journal of Econometrics, 2025, vol. 248, issue C

Abstract: In asset pricing models with stochastic volatility, uncertainty about volatility affects risk premia through two channels: aversion to decreasing returns and aversion to increasing volatility. We analyze the identification of and robust inference for structural parameters measuring investors’ aversions to these risks: the return risk price and the volatility risk price. In the presence of a leverage effect (instantaneous causality between the asset return and its volatility), we study the identification of both structural parameters with the price data only, without relying on additional option pricing models or option data. We analyze this identification challenge in a nonparametric discrete-time exponentially affine model, complementing the continuous-time approach of Bandi and Renò (2016). We then specialize to a parametric model and derive the implied minimum distance criterion relating the risk prices to the asset return and volatility’s joint distribution. This criterion is almost flat when the leverage effect is small, and we introduce identification-robust confidence sets for both risk prices regardless of the magnitude of the leverage effect.

Keywords: Leverage effect; Nonparametric identification; Stochastic volatility; Volatility factor; Volatility risk price; Weak identification (search for similar items in EconPapers)
JEL-codes: C12 C14 C38 C58 G12 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:248:y:2025:i:c:s030440762400294x

DOI: 10.1016/j.jeconom.2024.105943

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