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When allowing skewness in the returns of the underlier, certain differences to the base case emerge.
Assumptions include risk-averse behavior on the part of investors, constant volatility in the underlying asset, and a normal distribution of returns for the underlier.
I contribute to the literature on option maturity and expected returns with a detailed analysis of expected returns for both call and put options by maturity, both under standard asset pricing assumptions and after relaxing the assumptions of normality in returns and constant volatility of the underlier.
The first result for the random draw from the returns distribution of the underlier is a comparatively high 3.
Table 1 reports the call options returns statistics by moneyness and time to maturity when all the assumptions of Black-Scholes hold: the returns of the underlier are normally distributed and volatility is constant.
This beta is not to be confused with the standard option delta, which measures the sensitivity of the option price to changes in the price of the underlier.
Table 2 reports the put options returns statistics by moneyness and time to maturity when all the assumptions of Black-Scholes hold: the returns of the underlier are normally distributed and volatility is constant.
Therefore, the two sub-periods provide a great opportunity to study the effect on realized option returns of non-normality in the returns of the underlier.