The Statistical Properties of the Black–Scholes Option Price |
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| Authors: | Mthuli Ncube & Stephen Satchell |
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| Institution: | London School of Economics,;Trinity College, University of Cambridge |
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| Abstract: | This paper investigates the statistical properties of the Black–Scholes option price, considered as a random variable. The option is conditioned on the current price and/or the estimated volatility of the underlying security. In both cases, some exact results for the distribution functions of the true option price and the predicted option price are derived. Extensions to puts and American contracts are considered. Numerical results are presented for option prices based on parameters appropriate for the FTSE 100 Index. |
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| Keywords: | Black–Scholes option price put–call parity estimated option price smile effects |
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