  The purpose of this work is to explore the role that random 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.
