Stochastic arbitrage with market index options

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.