Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities

In this study we compare the quality and information content of risk neutral densities obtained by various methods. We consider a non-structural method, based on a mixture of log-normal densities, and the semi-nonparametric ones, based on an Hermite approximation of Abken, Madan, Milne, and Ramamurtie, or based on an Edgeworth expansion of Jarrow and Rudd. We also consider two structural approaches namely Malz, who assumes a jump-diffusion for the underlying process, and Heston's stochastic volatility model. We apply those models on FF/DM OTC exchange rate options for various dates ranging between May 1996 and June 1997 - covering the 1997 snap election. Models differ when important news hits the market (here the anticipated elections). The non-structural model provides a good fit to options prices but is unable to provide as much information about market participants' expectations as Malz's jump-diffusion model. Methods based on polynomial expansions have difficulties describing the exchange rate data at hand.