GARCH option pricing models and the variance risk premium

Wenjun Zhang and Jin E. Zhang

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.

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Year of publication:	2020
Authors:	Zhang, WenJun ; Zhang, Jin E.
Published in:	Journal of risk and financial management : JRFM. - Basel : MDPI, ISSN 1911-8074, ZDB-ID 2739117-6. - Vol. 13.2020, 3/51, p. 1-21
Subject:	GARCH option-pricing models \| stochastic volatility \| the CBOE VIX \| variance risk premium \| ARCH-Modell \| ARCH model \| Risikoprämie \| Risk premium \| Volatilität \| Volatility \| Optionspreistheorie \| Option pricing theory \| Optionsgeschäft \| Option trading \| Börsenkurs \| Share price