Relative Implied Volatility Arbitrage with Index Options

In the study reported here, we investigated the efficiency of markets as to the relative pricing of similar risk by using implied volatilities of options on highly correlated indexes and a statistical arbitrage strategy to profit from potential mispricings. We first analyzed the interrelationships over time of the three most highly correlated and liquid pairs of U.S. stock indexes. Based on this analysis, we derived a relative relationship between implied volatilities for each pair. If this relationship was violated (i.e., if we detected a relative implied-volatility deviation), we suspected a relative mispricing. We used a simple no-arbitrage barrier to identify significant deviations and implemented a statistical arbitrage trade each time such a deviation was recorded. We found that, although many deviations can be observed, only some of them are large enough to be exploited profitably in the presence of bid-ask spreads and transaction costs.