  We introduce a novel pricing kernel with time-varying variance risk aversion
that yields closed-form expressions for the VIX. We also obtain closed-form
expressions for option prices with a novel approximation method. The model can
explain the observed time-variation in the shape of the pricing kernel. We
estimate the model with S&P 500 returns and option prices and find that
time-variation in volatility risk aversion brings a substantial reduction in
derivative pricing errors. The variance risk ratio emerges as a fundamental
variable and we show that it is closely related to economic fundamentals and
key measures of sentiment and uncertainty.
