  The aim of this paper is to present a simple stochastic model that accounts
for the effects of a long-memory in volatility on option pricing. The starting
point is the stochastic Black-Scholes equation involving volatility with
long-range dependence. We consider the option price as a sum of classical
Black-Scholes price and random deviation describing the risk from the random
volatility. By using the fact the option price and random volatility change on
different time scales, we find the asymptotic equation for the derivation
involving fractional Brownian motion. The solution to this equation allows us
to find the pricing bands for options.
