Trading volatility spreads a test of index option market efficiency

The question of market efficiency is of great interest to practitioners and academics. For derivatives markets, many tests of market efficiency have examined arbitrage relationships; none, however, has attempted to test the efficiency of options markets regarding relative implied volatilities of highly correlated underlying assets—or, in other words, the relative pricing of similar risk.

This aspect of option market efficiency cannot be tested in a conventional way through the use of exact arbitrage relationships. Rather, a statistical arbitrage rule has to be applied. In the study reported here, we followed this approach to investigate the relative pricing of U.

First, from end-of-month March —December data, we ranked all pairs of U. We thus selected these three for the analysis. Second, we analyzed the interrelationship over time of the SPX—OEX, SPX—NYA, and OEX—NYA pairs by using rolling ordinary least-squares regressions of index returns and a robust minimum—maximum approach to determine high and low boundaries for regression coefficients.

Based on this analysis, we show that relative implied-volatility relationships can be derived for options with matching maturities. That is, given an observed implied volatility, we obtained low and high boundaries for the implied volatility of the option on the other index. If such a relationship was violated i. We measured implied volatility deviations from 3 January through 10 February and found that, although many deviations were observable, only a few of them were large enough to be used profitably in the presence of bid—ask spreads and transaction costs.

Therefore, to test an arbitrage trading strategy, we used an additional margin as a no-arbitrage barrier to account for spreads and trading costs.

The deviations that remained after we imposed this barrier we considered significant enough to allow the implementation of a potentially profitable statistical arbitrage trade. We implemented a statistical arbitrage trade for the period January through February every time such a deviation was newly recorded. Such situations occurred on 10 days for the SPX—OEX pair, on 37 days for the SPX—NYA pair, and on 28 days for the OEX—NYA pair.

The average holding time before relative volatilities were back within the no-arbitrage boundaries and the position was closed out was 2.

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On average, the trades were profitable for all index pairs after deduction of transaction costs. One losing trade occurred for the SPX—OEX pair, and six losing trades occurred for each of the other pairs. For all pairs, the average profit was larger than the average loss. With respect to profitability, however, because we used daily closing prices and assumed that trading would be possible at the signal price, not the tick following the signal price, we could not conclude with certainty that such a trading strategy would have generated exactly the same results in practice.

Overall, although the arbitrage strategy was profitable, we found too few potential arbitrage transactions to conclude that option markets are inefficient. Manuel Ammann is professor of finance at the University of St. Sylvan Herriger is an index derivatives trader at J.

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