  We consider a portfolio with call option and the corresponding underlying
asset under the standard assumption that stock-market price represents a random
variable with lognormal distribution. Minimizing the variance (hedging risk) of
the portfolio on the date of maturity of the call option we find a fraction of
the asset per unit call option. As a direct consequence we derive the
statistically fair lookback call option price in explicit form. In contrast to
the famous Black-Scholes theory, any portfolio can not be regarded as risk-free
because no additional transactions are supposed to be conducted over the life
of the contract, but the sequence of independent portfolios will reduce risk to
zero asymptotically. This property is illustrated in the experimental section
using a dataset of daily stock prices of 18 leading Australian companies for
the period of 3 years.
