The idea of term structure of "volatility"

Quiz 1: find an inductive argument showing that the volatility slope for at-the-money options should rise under fat tails. The "implied vols" of at-the-money options should be, say 20 for one year options, and 19 for the 3 month. More specifically, the higher the fourth moment of the distribution, the sharper the rise.

I will be away (and webless) until June 10 and will answer then. Ciao, NNT

Quiz 1-b - More complicated version of the argument: show that an infinite variance model should still produce a positively sloping volatility curve when seen under what people call "Black-Scholes" what we should call Bachelier-Thorp (short for Bachelier-Sprenkle-Boness-Thorp).