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An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks

Asmentioned in the introduction, the information associatedwith an event is represented by a data structure called a notification.We refer to the datamodel or encoding schema of notifications as the event notification model or simply event model. Most existing event notification services adopt a simple record- like structure for notifications, while some more recent frameworks define an object-oriented model (e.g., the Java™ Distributed Event Specification [Sun Microsystems 1998] and the CORBA Notification Service [Object Management Group 1998b]). Closely related to the eventmodel is the subscription language,which defines the form of the expressions associated with subscriptions. Two aspects of the subscription language are crucial to the issue of expressiveness | An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks Jun Liu Anderson School at UCLA Jun Pan MIT Sloan School of Management CCFR and NBER Tan Wang Sauder School of Business at UBC and CCFR This article studies the asset pricing implication of imprecise knowledge about rare events. Modeling rare events as jumps in the aggregate endowment we explicitly solve the equilibrium asset prices in a pure-exchange economy with a representative agent who is averse not only to risk but also to model uncertainty with respect to rare events. The equilibrium equity premium has three components the diffusive- and jump-risk premiums both driven by risk aversion and the rare-event premium driven exclusively by uncertainty aversion. To disentangle the rare-event premiums from the standard risk-based premiums we examine the equilibrium prices of options across moneyness or equivalently across varying sensitivities to rare events. We find that uncertainty aversion toward rare events plays an important role in explaining the pricing differentials among options across moneyness particularly the prevalent smirk patterns documented in the index options market. Sometimes the strangest things happen and the least expected occurs. In financial markets the mere possibility of extreme events no matter how unlikely could have a profound impact. One such example is the so-called peso problem often attributed to Milton Friedman for his comments about the Mexican peso market of the early 1970s. 1 Existing literature acknowledges the importance of rare events by adding a new type of risk We thank Torben Andersen David Bates John Cox Larry Epstein Lars Hansen John Heaton Michael Johannes Monika Piazzesi Bryan Routledge Jacob Sagi Raman Uppal Pietro Veronesi Jiang Wang an anonymous referee and seminar participants at CMU Texas Austin MD the 2002 NBER summer institute the 2003 AFA meetings the Cleveland Fed Workshop on Robustness and UIUC for helpful comments. We are .