Probability weighting functions implied in options prices |
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| Authors: | Valery Polkovnichenko Feng Zhao |
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| Affiliation: | 1. Federal Reserve Board, Division of Research and Statistics, Capital Markets MS-89, 20th & C street, Washington, DC 20551, United States;2. Naveen Jindal School of Management, University of Texas at Dallas, SM31, P.O.Box 830699, Richardson, TX 75083-0699, United States;1. Claremont McKenna College, Robert Day School of Economics and Finance, 500 E. 9th St., Claremont, CA 91711, USA;2. Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute, Quartier UNIL-Dorigny, 1015 Lausanne, Switzerland;1. Marshall School of Business, University of Southern California, Los Angeles, CA 90089, USA;2. Columbia Business School, Columbia University, New York, NY 10027, USA;3. Smeal College of Business, Pennsylvania State University, State College, PA 16802, USA;1. Columbia Business School, Uris Hall 805, Broadway 3022, NYC, NY 10027, United States;2. Columbia Business School, Uris Hall 810, Broadway 3022, NYC, NY 10027, United States;3. Haas School of Business, University of California, Berkeley, 545 Student Services Building #1900, Berkeley, CA 94720-1900, United States |
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| Abstract: | The empirical pricing kernels estimated from index options are non-monotone (Rosenberg and Engle, 2002, Bakshi et al., 2010) and the corresponding risk-aversion functions can be negative (Aït-Sahalia and Lo, 2000, Jackwerth, 2000). We show theoretically that these and several other properties of empirical pricing kernels are consistent with rank-dependent utility model with probability weighting function, which overweights tail events. We also estimate the pricing kernels nonparametrically from the Standard & Poor's 500 index options and construct empirical probability weighting functions. The estimated probability weights typically have the inverse-S shape, which overweights tail events and is widely supported by the experimental decision theory. |
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