The Risk Premia Embedded in Index Options (AQR Insight Award Winner)

May 2014

KEYWORDS: stock, risk, Equity markets, tail risk, Volatility, market risk, risk premium


Torben G. Andersen, Ph.D.; Nicola Fusari, Ph.D.; Viktor Todorov, Ph.D.


We study the dynamic relation between aggregate stock market risks and risk premia via an exploration of the time series of equity-index option surfaces. The analysis is based on estimating a general parametric asset pricing model for the risk-neutral equity market dynamics using a panel of options on the S&P 500 index, while remaining fully nonparametric about the actual evolution of market risks. We find that the risk-neutral jump intensity, which controls the pricing of left tail risk, cannot be spanned by the market volatility (and its components), so an additional factor is required to account for its dynamics. This tail factor has no incremental predictive power for future equity return volatility or jumps beyond what is captured by the current and past level of volatility. In contrast, the novel factor is critical in predicting the future market excess returns over horizons up to one year, and it explains a large fraction of the future variance risk premium. We contrast our findings with those implied by structural asset pricing models that seek to rationalize the predictive power of option data. Relative to those studies, our findings suggest a wider wedge between the dynamics of equity market risks and the corresponding risk premia with the latter typically displaying a far more persistent reaction following market crises.

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