NotQuiteRandom
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The issue of 'why' for the vol skew is much debated but, as you say, the empirical evidence is that it compensates for the high degree of second order volatility in asset markets. Before 1987 people were assuming a lognormal Black-Scholes framework.
I've been testing the BetaExoticBets.com/enter/ site out that T2W emailed earlier and trading lookbacks on there. Obviosly more (about double) the time premium to vanillas but you get the payoff which is the difference between the strike and the best price at expiry, not the spot price at expiry. Very cool!
I just reverse engineered their implied vols and found that they were only just above the market. On the FX ones they were less than half a point above.
Have you tried these?
NQR
I've been testing the BetaExoticBets.com/enter/ site out that T2W emailed earlier and trading lookbacks on there. Obviosly more (about double) the time premium to vanillas but you get the payoff which is the difference between the strike and the best price at expiry, not the spot price at expiry. Very cool!
I just reverse engineered their implied vols and found that they were only just above the market. On the FX ones they were less than half a point above.
Have you tried these?
NQR