Relative Implied Volatility Arbitrage with Index Options

Abstract

We investigate statistical arbitrage strategies for index options. To test the efficiency of markets in pricing relative implied volatilities in highly correlated markets, U.S. stock indices for which listed options are available are matched into pairs according to their degree of correlation. The interrelationship over time of the three most highly correlated and liquid index pairs is then analyzed. Based on this analysis, the relative implied volatility relationships are calculated. If such a relationship is violated, a relative mispricing is identified. We find that, although many theoretical mispricings can be observed, only a fraction of them are large enough to be used profitably in the presence of bid-ask spreads and transaction costs. A simple no-arbitrage barrier is thus used to identify significant mispricings and a statistical arbitrage trade is implemented every time such a mispricing was recorded, the trades being on average profitable after deduction of transaction costs.