Quiz 2

I leave Part 2 of Quiz 1 for another day (it requires some redefinition of volatility outside of the norm L2).

The new quiz. When I tell people that a mixture of distributions (assume Gaussian, with no too much loss of generality) generally produces fat tails, not thin tails, I mean "generally", not always. What are the exceptions? What are the situations in which the ATM options should trade at higher "volatility" (in terms of the Bachelier-Thorp language, known by most as the Black-Scholes equation)? In other world when should the smile trade like a "/\" not a "V"?

This to me is monstrously practical. I haven't seen many people cracking the problem. I've quizzed many.

Ciao, NNT