The empirical performance of option-based densities of foreign exchange

In this paper, the authors calculate risk-neutral densities (RND) by estimating the daily diffusion process of the underlying futures contract for foreign exchange, based on the price of the American puts and calls reported on the Chicago Mercantile Exchange for the end of the day. Their quick and accurate method of calculating the prices of the American options uses higher-order lattices and smoothing of the option's value function at the boundaries to mitigate the nondifferentiability of the payoff boundary at expiration and the early exercise boundary. The authors estimate the diffusion process by minimizing the squared distance between the calculated prices and the observed prices in the data.