Time series evidence on exchange rates has been unable to reject the random walk hypothesis. A simple structural model that accounts for target zone nonlinearities provides conclusive evidence of mean reversion in EMS exchange rates.

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...