Option Pricing with Time-Varying Volatility Risk Aversion (2204.06943v3)

Abstract: We introduce a pricing kernel with time-varying volatility risk aversion that can explain the observed time variation in the shape of the pricing kernel. Dynamic volatility risk aversion, combined with the Heston-Nandi GARCH model, leads to a convenient option pricing model, denoted DHNG. The variance risk ratio emerges as a fundamental variable, and we show that it is closely related to economic fundamentals and common measures of sentiment and uncertainty. DHNG yields a closed-form pricing formula for the VIX, and we propose a novel approximation method that provides analytical expressions for option prices. We estimate the model using S&P 500 returns, the VIX, and option prices, and find that dynamic volatility risk aversion leads to a substantial reduction in VIX and option pricing errors.