Tractable conditions for stochastic arbitrage in index options: Theory and evidence

This study develops and applies tractable conditions for stochastic arbitrage in equity index options. The conditions, derived from the dual formulation of asset pricing restrictions, take the form of a relatively small set of linear inequalities and can incorporate bid-ask spreads and potential portfolio constraints. Because return distributions vary across volatility regimes, the inequalities must be tested conditionally, as unconditional tests cannot establish market inefficiency. Using the proposed arbitrage conditions and statistical dominance tests, we reexamine efficiency in one-month S&P 500 index options. Out-of-sample performance analysis points at arbitrage opportunities in high-volatility regimes, predominantly in the form of call front spreads. These opportunities often remain undetected unless both the volatility dependence of the market risk premium and the negative conditional skewness of index returns are taken into account. When volatility is low to moderate, no significant arbitrage opportunities are detected, consistent with higher pricing efficiency.