  Opportunities for stochastic arbitrage in an options market arise when it is
possible to construct a portfolio of options which provides a positive option
premium and which, when combined with a direct investment in the underlying
asset, generates a payoff which stochastically dominates the payoff from the
direct investment in the underlying asset. We provide linear and mixed-integer
linear programs for computing the stochastic arbitrage opportunity providing
the maximum option premium to an investor. We apply our programs to 18 years of
data on monthly put and call options on the Standard & Poors 500 index,
confining attention to options with moderate moneyness, and using two
specifications of the underlying asset return distribution, one symmetric and
one skewed. The pricing of market index options with moderate moneyness appears
to be broadly consistent with our skewed specification of market returns.
