An Equilibrium Model of Rare Event Premia

22 Pages Posted: 31 May 2002

See all articles by Jun Liu

Jun Liu

University of California, San Diego (UCSD) - Rady School of Management

Tan Wang

University of British Columbia (UBC) - Division of Finance; China Academy of Financial Research (CAFR)

Jun Pan

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF); National Bureau of Economic Research (NBER); China Academy of Financial Research (CAFR)

Date Written: May 21, 2002

Abstract

In this paper, we study 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. Our results show that there are three components in the equity premium: the diffusive-risk premium, the jump-risk premium, and the "rare event premium." While the first two premia are generated by risk aversion, the last one is driven exclusively by uncertainty aversion. To disentangle the "rare event premium" from the standard risk-based premia, we examine the equilibrium prices of options with varying degree of moneyness. We consider models with different levels of uncertainty aversion - including the one with zero uncertainty aversion, and calibrate all models to the same level of equity premium. Although observationally equivalent with respect to the equity market, these models provide distinctly different predictions on the option market. Without incorporating uncertainty aversion, the standard model cannot explain the extent of the premia implicit in options, particularly the prevalent "smirk" patterns documented in the index options market. In contrast, the models incorporating uncertainty aversion can generate significant premia for at-the-money option prices, as well as pronounced "smirk" patterns for options with different degrees of moneyness.

Suggested Citation

Liu, Jun and Wang, Tan and Pan, Jun, An Equilibrium Model of Rare Event Premia (May 21, 2002). MIT Sloan Working Paper No. 4370-02; AFA 2003 Washington, DC Meetings, Sauder School of Business Working Paper, Available at SSRN: https://ssrn.com/abstract=313205 or http://dx.doi.org/10.2139/ssrn.313205

Jun Liu

University of California, San Diego (UCSD) - Rady School of Management ( email )

9500 Gilman Drive
Rady School of Management
La Jolla, CA 92093
United States
858.534.2022 (Phone)
5858.534.0745 (Fax)

Tan Wang

University of British Columbia (UBC) - Division of Finance ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada
604-822-9414 (Phone)
604-822-8521 (Fax)

China Academy of Financial Research (CAFR)

1954 Huashan Road
Shanghai P.R.China, 200030
China

Jun Pan (Contact Author)

Shanghai Jiao Tong University (SJTU) - Shanghai Advanced Institute of Finance (SAIF) ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

China Academy of Financial Research (CAFR)

1954 Huashan Road
Shanghai P.R.China, 200030
China

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