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We test the Index options market efficiency by means of a statistical arbitrage strategy, i.e. pairs trading. Using data on five Index Option Markets of the Euro Area, we first identify any potential option mispricing based on deviations from the long-run relationship linking their implied volatilities. Then, we evaluate the profitability of a simple pair trading strategy on the mispriced options. Despite the fact that the signals of potential mispricing are frequent, the statistical arbitrage does not produce significant profits, thus providing evidence in support of Index Option market efficiency. The results, which remain unchanged in a variety of robustness checks, also prove that the observed profits are strongly associated to the moneyness of the options traded while they do not correlate to options’ maturity or to financial market turbulence.