Option Prices in a Model with Stochastic Disaster Risk

63 Pages Posted: 9 Nov 2013

See all articles by Sang Byung Seo

Sang Byung Seo

University of Wisconsin - Madison

Jessica A. Wachter

University of Pennsylvania - Finance Department; National Bureau of Economic Research (NBER)

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Date Written: November 2013

Abstract

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.

Suggested Citation

Seo, Sang Byung and Wachter, Jessica A., Option Prices in a Model with Stochastic Disaster Risk (November 2013). NBER Working Paper No. w19611, Available at SSRN: https://ssrn.com/abstract=2352128

Sang Byung Seo (Contact Author)

University of Wisconsin - Madison ( email )

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Jessica A. Wachter

University of Pennsylvania - Finance Department ( email )

The Wharton School
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United States
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National Bureau of Economic Research (NBER)

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