Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data |
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| Institution: | 1. Kent Business School, University of Kent, Canterbury, United Kingdom;2. Department of Mathematical Sciences, University of Essex, United Kingdom;1. European Central Bank, Directorate General Economics, Monetary Policy, Capital Markets and Financial Structures Division, Sonnemannstr. 20, 60314 Frankfurt, Germany;2. University of Duisburg-Essen, Faculty for Economics and Business Administration, Department of Financial Market Econometrics, Universitaetsstr. 12, 45117 Essen, Germany;1. Freie Universität Berlin, Department of Economics, D-14195 Berlin, Germany;2. University of Regensburg, Department of Economics and Econometrics, D-93040 Regensburg, Germany;3. Institute for Employment Research (IAB), Germany;4. IOS Regensburg, Germany;1. De Nederlandsche Bank, Amsterdam, The Netherlands;2. Florida State University, Tallahassee, FL, USA;1. University of Central Florida, Orlando, FL, United States;2. Fordham University, Bronx, NY, United States |
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| Abstract: | As a means of validating an option pricing model, we compare the ex-post intra-day realized variance of options with the realized variance of the associated underlying asset that would be implied using assumptions as in the Black and Scholes (BS) model, the Heston, and the Bates model. Based on data for the S&P 500 index, we find that the BS model is strongly directionally biased due to the presence of stochastic volatility. The Heston model reduces the mismatch in realized variance between the two markets, but deviations are still significant. With the exception of short-dated options, we achieve best approximations after controlling for the presence of jumps in the underlying dynamics. Finally, we provide evidence that, although heavily biased, the realized variance based on the BS model contains relevant predictive information that can be exploited when option high-frequency data is not available. |
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| Keywords: | Option pricing High frequency data Realized variance Stochastic volatility Jump diffusion |
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