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GARCH Option Pricing Models and the Variance Risk Premium

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  • Wenjun Zhang

    (Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Auckland 1142, New Zealand)

  • Jin E. Zhang

    (Department of Accountancy and Finance, Otago Business School, University of Otago, Dunedin 9054, New Zealand)

Abstract

In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than in the physical one, so that one is able to capture the variance risk premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use our mLRNVR when pricing options with GARCH models.

Suggested Citation

  • Wenjun Zhang & Jin E. Zhang, 2020. "GARCH Option Pricing Models and the Variance Risk Premium," JRFM, MDPI, vol. 13(3), pages 1-21, March.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:3:p:51-:d:330107
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    References listed on IDEAS

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    Cited by:

    1. 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.

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