Working Papers, Department of Economics, Rutgers, The State University of New Jersey 1996-10
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 anomaly. I develop a simulated method of moments estimation procedure. I parameterize the underlying exchange rate process as a mixture of log-normals, price the options using Monte Carlo methods, and compare these simulated price 'moments' to the market data. This process switching model appears to be quite promising in explaining the volatility smile. Applying this to the ERM data, I find that the probability of a devaluation in the British Pound almost doubled before it withdrew from the ERM. This risk becomes statistically significant on September 15, 1992, only one day prior to the crisis though. The French Franc crisis of July-August 1993 appears to have been better anticipated. By July 20, 1993, the model predicts with 95% confidence that the Franc is going to be devalued.
devaluation ERM implied distribution options volatility smile