Risk premium and rough volatility

Ofelia Bonesini; Antoine Jacquier; Aitor Muguruza

doi:10.3934/fmf.2025013

Article Contents

December 2025, Volume 7, 78-94. Doi: 10.3934/fmf.2025013 Free Access

This volume Previous Article The term structure of implied correlations between S&P and VIX markets Next Article Filtration reduction and completeness in Brownian motion models

Risk premium and rough volatility

1.
Department of Mathematics, London School of Economics and Political Science, United Kingdom
2.
Department of Mathematics, Imperial College London, United Kingdom
3.
Department of Mathematics, Imperial College London and Kaiju Capital Management, United Kingdom

^*Corresponding author: Antoine Jacquier
^*Corresponding author: Antoine Jacquier

Received: March 18, 2025

Revised: June 13, 2025

Published online: December 11, 2025

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Abstract

On the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility risk is a well-studied object in financial economics, and empirical estimates show it to be stochastic rather than deterministic. Starting from a rough volatility model under the historical measure, we take up this challenge and provide an analysis of the impact of such a non-deterministic risk for pricing purposes.

Keywords:

Mathematics Subject Classification: 60G15, 60G22, 91G20.

Citation:

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Figure 1. Variance swap volatility daily quotes on SX5E

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Figure 2. Forward variances extracted from variance swap quotes on SX5E

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Figure 3. Annualized daily realized volatility on SX5E

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Figure 4. Estimated $ \widehat{H} $ and $ \widehat{\nu} $ on SX5E

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Figure 5. Daily correlation estimate on SX5E and realized volatility

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Figure 6. Daily SX5E risk premia; dashed lines represent means

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