Disasters Implied by Equity Index Options

Abstract

We use equity index options to quantify the probability and magnitude of disasters: extreme negative realizations of consumption growth and stock returns. We show that option prices imply smaller probabilities of these extreme outcomes than have been estimated from international macroeconomic data. A useful byproduct is a novel characterization of departures from lognormality in asset pricing models based on high-order cumulants: skewness, excess kurtosis, and so on. JEL Classification Codes: E44, G12.

The cross-section and time series of stock and bond returns

“…Finally, there is a related literature that studies the temporal composition of risk in asset prices, including Cochrane and Hansen (1992), Kazemi (1992), Bansal and Lehman (1997), Hansen, Heaton, and Li (2008), Alvarez andJermann (2004, 2005), Hansen and Scheinkman (2009), Borovicka, Hansen, Hendricks, and Scheinkman (2009), Martin (2008, Backus, Routledge, and Zin (2008), and Backus, Chernov, and Martin (2009). Our model connects to this discussion because it features both permanent shocks (to aggregate dividend) and transitory shocks (to real economic activity).…”

Realized Skewness

“…It would also be nice to be able to extend the analysis to higher order moments (or indeed to the cumulants of the distribution as in Backus, Chernov and Martin (2011)). This would not be straightforward; as Proposition 2 shows, the set of functions that possess the Aggregation Property is quite limited; the way forward here may be to include other traded claims in addition to those on the variance of the distribution.…”

“…These findings are relevant to the debate on the role of large disasters in explaining the equity premium. In reviewing the evidence, Backus, Chernov andMartin (2011, p1970, "BCM") note that "in virtually all of this research [starting with Rietz (1988), followed by Longstaff and Piazzesi (2004), Barro (2009) and others], the distribution [of log returns] is modeled by combining a normal component with a jump component. The jump component, in this context, is simply a mathematical device that produces nonnormal distributions".…”

“…The literature going back to Kraus and Litzenberger (1976), and including more recently Harvey and Siddique (2000), Ang, Hodrick, Xing and Zhang (2006), Ang, Cheng and Xing (2006) and Xing, Zhang and Zhao (2010), suggests that the asymmetry of the returns distribution both for individual stocks and for the market as a whole is important for asset pricing and investment management. Skewness is central to the debate on the role of large rare disasters in explaining the equity risk premium (Rietz (1988), Longstaff and Piazzesi (2004), Barro (2009), andBackus, Chernov andMartin (2011)). Carr and Wu (2007) document the time varying implied skew in foreign exchange markets, and Brunnermeier, Nagel and Pedersen (2008) relate the forward premium puzzle to the skewed distribution of currency returns.…”

Disaster Risk and Asset Returns: An International Perspective

“…Martin (2008) solves for the welfare cost of business cycles due to disasters, but does not match to asset return data. Backus, Chernov, and Martin (2011) use U.S. equity index options to examine the implied disaster risk in consumption. Gourio (2008Gourio ( , 2012 evaluates the impact of disasters in a real business cycle model allowing for recoveries after a disaster.…”