Disaster Risk and Its Implications for Asset Pricing

Abstract

After laying dormant for more than two decades, the rare disaster framework has emerged as a leading contender to explain facts about the aggregate market, interest rates, and financial derivatives. In this paper we survey recent models of disaster risk that provide explanations for the equity premium puzzle, the volatility puzzle, return predictability and other features of the aggregate stock market. We show how these models can also explain violations of the expectations hypothesis in bond pricing, and the implied volatility skew in option pricing. We review both modeling techniques and results and consider both endowment and production economies. We show that these models provide a parsimonious and unifying framework for understanding puzzles in asset pricing.

Solution methods for models with rare disasters

“…Many researchers have followed Barro's lead and formulated, calibrated/estimated, and solved models with disaster probabilities and declines in consumption that are roughly in agreement with Barro's original proposal, including among others, Barro and Ursúa (2012), Barro and Jin (2011), Nakamura, Steinsson, Barro, and Ursúa (2013), Wachter (2013), and Tsai and Wachter (2015). The approach has also been extended to analyze business cycles (Gourio (2012)), credit risk (Gourio (2013)), and foreign exchange markets (Farhi and Gabaix (2016) and Gourio, Siemer, and Verdelhan (2013)).…”

Discounting the Future: on Climate Change, Ambiguity Aversion and Epstein-Zin Preferences

“…Extensions to the early disaster/jump risk models are the use of Stochastic Differential Utility (SDU) instead of power utility, and the introduction of time-varying disaster probabilities and multi-period (i.e. persistent) disasters (Barro (2009);Wachter (2013); Tsai and Wachter (2015)). Climate change induced disasters fit in the rare disaster literature since climate change is increasingly thought to give rise to large and abrupt destructive changes in the Earth's environment (Goosse, 2015) whose occurrence has a small probability at any given moment of time but with possibly large negative effects on the economy.…”

“…Our stochastic and preference structure combines the model of Liu et al (2004) with ambiguity aversion with respect to the parameters of the jump-risk component, with the i.i.d. model of Tsai and Wachter (2015). This implies that the agent has SDU preferences, the stochastic consumption process follows a jump diffusion process and the representative agent is ambiguity averse with respect to the arrival rate and the jump probability of the jump-risk component.…”

“…This is the reason why we adopt the Stochastic Differential Utility framework introduced by Duffie and Epstein (1992b) since with SDU the risk aversion parameter and the elasticity of intertemporal substitution (EIS) are no longer restricted to be each other's inverse. Furthermore, we go beyond the setting of Tsai and Wachter (2015) by introducing ambiguity aversion. This extension can also be relevant in the general disaster model, but is especially relevant in the climate disaster model since there is no clear history of events on which we can base our estimates of the damages.…”

A Likelihood-Based Comparison of Macro Asset Pricing Models

“…As the residual represents excess volatility, it naturally maps to hard-toobserve variations in risk. This kind of modeling has the virtue of being highly tractable, and thus leads to explicit predictions about a variety of asset market phenomena (Tsai and Wachter (2015)).…”