Does the term structure of the at-the-money skew really follow a power law?
A power law can fit the ATM skew, but struggles with short maturities
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Using two years of Standard & Poor’s 500, Eurostoxx 50 and DAX data, Mehdi El Amrani and Julien Guyon empirically investigate the term structure of the at-the-money forward skew of equity indexes. While a power law (two parameters) captures the term structure accurately beyond short maturities, the power-law fit deteriorates considerably when short maturities are included. By contrast, three-parameter shapes that look like power laws but do not blow up at
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