Options market efficiency is a topic of interest not only to academics but also to practitioners. There is a body of research focusing on market inefficiency. For example, we recently highlighted a research paper dealing with sector ETFs’ implied volatilities and correlations. The research result implies that the options market is not efficient, as one can earn extra returns by using trading signals generated from the implied correlation premium.

There is, however, an opposite school of thought that promotes the idea that the options market is efficient and excess returns cannot be earned. A recent example is Reference [1] in which the authors calculated the index options implied volatilities and used them to generate trading signals,

*We test the Index options market efficiency by means of a statistical arbitrage strategy, i.e. pairs trading. Using data on five Stock Indexes 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. *

The article went on to conclude that the index options market is efficient,

*Using data on one-month maturity ATM call options written on five European Indexes, over the 2007-2019 period, we find that arbitrage opportunities, despite frequent, are short-lived and mostly lead to non-significant profits, in both the self-financing strategy (in which the quantities traded in the two stocks are such that no initial capital investment is required) and in the beta-arbitrage (in which the quantities traded are a function of the regression slope estimates). Market forces are thus able to quickly identify and reabsorb potential mispricing, further confirmed by the fact that the average trade closes within 4 days.* *Consistently with previous works on European index option market (Capelle Blancard and Chaudhury, 2001, Mittnik and Rieken, 2000, Cavallo and Mammola, 2000, and Brunetti and Torricelli, 2005), our final conclusion is in favor of index option market efficiency. *

We respect the authors’ research effort and conclusion, and we will consider their results in our trading strategy development process. However, we’d like to point out that the PnL drivers of an index options pair are the constituents’ not only implied volatilities but also realized volatilities. The authors did not take into account the realized volatilities explicitly when generating trading signals and constructing the option positions. The realized volatilities were taken into account implicitly as they manifested themselves through the moneyness of options,

*Investigating the main drivers of options’ pair trading, we find that the realized returns are mostly driven by the moneyness of both the options involved. Consistently with expectations, the strategy returns are on average higher whenever the option sold is OTM and/or the option on which a long position is taken is ITM, while on average lower when the sold option is ITM and/or the option bought is OTM.*

If the authors took into account the realized volatilities in their strategy development process, the results might have been different.

Notwithstanding the efficient market debate, constructing options positions to take advantage of the mispricings (if any) is not trivial.

**References**

[1] M. Brunetti, R. De Luca, *Pairs trading in the index options market, *efmaefm.org, 2020