The Pricing of Tail Risk and the Equity Premium: Evidence from International Option Markets
(with Torben G. Andersen and Viktor Todorov)
We show evidence that a tail factor extracted from the option market predicts future market returns in both US and many of the european markets. Most importantly this factor is embedded in the dynamics of option prices but not in the time series of stock prices, showing the importance of the derivatives market in embedding beliefs about possible future market downturns.
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The paper explores the global pricing of market tail risk as manifest in equity-index options. We document the presence of a left tail factor that displays large persistent shifts, largely unrelated to the corresponding dynamics of return volatility. This left tail factor is a potent predictor of future excess equity-index returns, while the implied volatility only forecasts future equity return variation, not the expected returns. We conclude that the option surface embeds separate equity risk and risk premium factors which are successfully disentangled by our simple two-factor affine model for all the equity indices explored. The systematic deviations across countries speak to the differential risk and its pricing during the great recession and the European sovereign debt crises. Most strikingly, the relative tail risk pricing displays pronounced heterogeneity for the Southern European countries. During the sovereign debt crisis, their stock markets react almost identically to Euro-wide systematic shock, but these events are priced very differently in the respective option markets, indicating differences in crash beliefs across countries which are hard to detect with stock market data alone.