Option prices seem to behave in ways inconsistent with the Black-Scholes model. Implied volatility varies with the strike price in a parabolic shape that is often called the volatility 'smile.' My objective in this paper is to identify implied probability distributions that might explain this...

We use futures instead of forward rates to study the complete maturity spectrum of the forward premium puzzle from two days to six months. At short maturities the slope coefficient is positive, but these turn negative as the maturity increases to the monthly level. Futures data allow us to...