  The purpose of this work is to explore the role that arbitrage opportunities
play in pricing financial derivatives. We use a non-equilibrium model to set up
a stochastic portfolio, and for the random arbitrage return, we choose a
stationary ergodic random process rapidly varying in time. We exploit the fact
that option price and random arbitrage returns change on different time scales
which allows us to develop an asymptotic pricing theory involving the central
limit theorem for random processes. We restrict ourselves to finding pricing
bands for options rather than exact prices. The resulting pricing bands are
shown to be independent of the detailed statistical characteristics of the
arbitrage return. We find that the volatility "smile" can also be explained in
terms of random arbitrage opportunities.
