Premium
The Statistical Properties of the Black–Scholes Option Price
Author(s) -
Ncube Mthuli,
Satchell Stephen
Publication year - 1997
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00033
Subject(s) - black–scholes model , valuation of options , implied volatility , call option , economics , econometrics , stochastic volatility , volatility (finance) , put option , asian option , volatility smile , mathematics , mathematical economics , financial economics
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.