This is more difficult.

A Vanilla European Put on a stock or a currency is assumed to "always" have negative delta. Bogus! What are the situations in which the delta is going to be positive (delta as conventionally used --it applies to both the spot and the forward)?

I think that I have 100 of these questions.

Part 1

assume p1=p2=1/2

Answers

The graph. You can see k the kurtosis droping with |m1-m2| (means diverging) but rising with |s1-s2| (standard deviations diverging).

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