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Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model

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  • Petra Posedel Šimović

    (Department of Informatics and Mathematics, University of Zagreb Faculty of Agriculture, 10000 Zagreb, Croatia)

  • Azra Tafro

    (University of Zagreb Faculty of Forestry and Wood Technology, 10000 Zagreb, Croatia)

Abstract

Investors’ decisions on capital markets depend on their anticipation and preferences about risk, and volatility is one of the most common measures of risk. This paper proposes a method of estimating the market price of volatility risk by incorporating both conditional heteroscedasticity and nonlinear effects in market returns, while accounting for asymmetric shocks. We develop a model that allows dynamic risk premiums for the underlying asset and for the volatility of the asset under the physical measure. Specifically, a nonlinear in mean time series model combining the asymmetric autoregressive conditional heteroscedastic model with leverage (NGARCH) is adapted for modeling return dynamics. The local risk-neutral valuation relationship is used to model investors’ preferences of volatility risk. The transition probabilities governing the evolution of the price of the underlying asset are adjusted for investors’ attitude towards risk, presenting the asset returns as a function of the risk premium. Numerical studies on asset return data show the significance of market shocks and levels of asymmetry in pricing the volatility risk. Estimated premiums could be used in option pricing models, turning options markets into volatility trading markets, and in measuring reactions to market shocks.

Suggested Citation

  • Petra Posedel Šimović & Azra Tafro, 2021. "Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model," Mathematics, MDPI, vol. 9(17), pages 1-15, August.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2038-:d:621163
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    2. Xianfei Hui & Baiqing Sun & Hui Jiang & Yan Zhou, 2022. "Modeling dynamic volatility under uncertain environment with fuzziness and randomness," Papers 2204.12657, arXiv.org, revised Oct 2022.

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