What Does Derivative and Credit Markets Tell Us about Rare Consumption Disasters?

While there is mounting evidence that macroeconomic disaster - infrequent large declines in aggregate output and consumption - produce dramatic improvement in the ability of pricing models to reproduce prominent features of US asset returns, the primary challenge for such researches lies in estimating their probability and magnitude. One apparent reason is that disaster events are infrequent and are often absent in small samples. Barro (2009), for example, document that the occurrence of jumps in consumption are minor in the post-WWII period for the US and most of the OECD countries. This scarcity complicates the identification of the expected magnitude and likelihood of consumption disasters.In this study, instead of relying on realizations of consumption time series as have been the case for many prior researches, we follow a complementary path and use both equity index options and credit market instruments to infer the distribution of extreme events as well as risk aversion. The crucial advantage of our proposed approach is that participants in these markets value extreme events, whether they happen in our sample or not.It is widely recognized that prices of both deep-out-of-the-money equity index options and senior CDX tranches are only sensitive to disaster like events. This property provides econometric power to identify the unconditional distribution consumption disaster as well as their representative agent risk aversion. To our knowledge there is no empirical study that has utilized information jointly from both markets to pin down the disaster and preference parameters.To this end, we develop a consumption-based equilibrium model while accounting for disaster component in consumption that is capable of jointly pricing equity index options and credit index tranches while matching the equity premium. We rely on the generalized method of moments to pin down the expected disaster probabilities and magnitude. We will demonstrate the econometric advantage of relying on credit instrument to complement the range of available traded OTM option prices. By fitting the model separately to each market at a time, we will be able to examine the degree of heterogeneity between the credit, stock and option market participant concerning disaster expectations. Our model will also allow us to capture the changing nature in expectation of the severe systematic crash before and after the recent market turmoil. We expect our study to deliver the resonable P-estimates of expected disaster probabilities and magnitude reflected in the financial market for both economists and policy makers.