The use of option prices in order to evaluate the skewness risk premium

The objectives of this study are twofold. First, to determine the sign and to assess the magnitude of the skewness risk premium (SRP) in the Italian index option market using two methods: (i) skewness swap contracts, and (ii) option trading strategies. Second, to investigate the behavior of the skewness risk premium for short and medium-term maturities in order to provide investors with a proper time horizon for skewness trading strategies. Several results are obtained. First, the SRP, defined as the difference between the physical and the risk-neutral measure of skewness, is positive and it is both statistically and economically significant. This indicates that SRP does exists, it is positive in sign, and it can be quantified. Second, SRP is the highest in magnitude for the 30-day maturity (€35 on a €100 of notional) while it is lower for 60-day and 90-day maturity (both close to €27 on a €100 of notional). Third, skewness trading strategies confirm our finding of a positive and economically significant risk premium for skewness. In particular, the profitability of trading strategies is concentrated on the left tail of the distribution, suggesting a considerable overvaluation of out-of-the-money put options. Fourth, as regards the proper time horizon for skewness trading, we find that a strategy that sells out-of-the-money puts is more profitable, if options with maturity ranging from 30 to 70 days are used. On the other hand, a strategy that takes a long position in out-of-the-money calls, and a short position in out-of-the-money puts, yields a higher return, if options with short-term maturity are used. This suggests that investors are more averse to tail risk for short-term horizons than they are for medium-term horizons.