Option Prices in a Model with Stochastic Disaster Risk
Contrary to the Black-Scholes model, volatilities implied by index option prices depend on the exercise price of the option and are often higher than realized volatilities. We explain both facts in the context of a model that can also explain the mean and volatility of equity returns. Our model assumes a small risk of a rare disaster that is calibrated based on the international data on large consumption declines. We allow the risk of this rare disaster to be stochastic, which turns out to be crucial to the model's ability to explain both equity volatility and option prices. We explore different specifications for the stochastic rare disaster probability and show that the data favor a multifrequency process. Finally, we show that the model can simultaneously fit the time series of option prices and equities.
We thank Hui Chen, Domenico Cuoco, Mikhail Chernov, Xavier Gabaix, Ivan Shaliastovich, Viktor Todorov and seminar participants at the 2013 NBER Summer Institute, Carnegie Mellon University, Cornell University and the Wharton school for helpful comments. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Sang Byung Seo & Jessica A. Wachter, 2019. "Option Prices in a Model with Stochastic Disaster Risk," Management Science, vol 65(8), pages 3449-3469.