An Equilibrium Model of Rare Event Premia
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...
| Main Authors: | , , |
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| Language: | en_US |
| Published: |
2002
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/1575 |
| _version_ | 1826188147968442368 |
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| author | Liu, Jun Pan, Jun Wang, Tan |
| author_facet | Liu, Jun Pan, Jun Wang, Tan |
| author_sort | Liu, Jun |
| collection | MIT |
| description | 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 dis-entangle 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. |
| first_indexed | 2024-09-23T07:55:18Z |
| id | mit-1721.1/1575 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:55:18Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | mit-1721.1/15752019-04-09T15:32:25Z An Equilibrium Model of Rare Event Premia Liu, Jun Pan, Jun Wang, Tan Asset Prices Event Premia Equilibrium Model 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 dis-entangle 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. 2002-08-12T19:10:44Z 2002-08-12T19:10:44Z 2002-08-12T19:10:54Z http://hdl.handle.net/1721.1/1575 en_US MIT Sloan School of Management Working Paper;4370-02 185651 bytes application/pdf application/pdf |
| spellingShingle | Asset Prices Event Premia Equilibrium Model Liu, Jun Pan, Jun Wang, Tan An Equilibrium Model of Rare Event Premia |
| title | An Equilibrium Model of Rare Event Premia |
| title_full | An Equilibrium Model of Rare Event Premia |
| title_fullStr | An Equilibrium Model of Rare Event Premia |
| title_full_unstemmed | An Equilibrium Model of Rare Event Premia |
| title_short | An Equilibrium Model of Rare Event Premia |
| title_sort | equilibrium model of rare event premia |
| topic | Asset Prices Event Premia Equilibrium Model |
| url | http://hdl.handle.net/1721.1/1575 |
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