exposures. Using data for the trading activities in the market of deep out-of-the-money S&P 500 put options, we identify periods …

the international data on large consumption declines. We allow the risk of this rare disaster to be stochastic, which … specifications for the stochastic rare disaster probability and show that the data favor a multifrequency process. Finally, we show …

conforms with data from 1983 to 2015 on far-out-of-the-money put options on the U.S. S&P 500 and analogous indices for other … countries. The analysis uses two types of data—indicative prices on OTC contracts offered by a large financial firm and market … data provided by OptionMetrics, Bloomberg, and Berkeley Options Data Base. The options-pricing formula involves a …