Exact Solution of Discrete Hedging Equation for European Option

Abstract

The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough classes of distribution functions too. It is shown that there exists a nonzero possibility that market parameters can take values such that to realize the hedging policy becomes impossible. This fact is not in contradiction with Black-Scholes option price model as long as this possibility tends to zero at the limit of continuous hedging.