Security prices contain valuable information that can be used to make a wide variety of economic decisions. To extract this information, a model is required that relates market prices to the desired information, and that ideally can be implemented using timely and low-cost methods. The authors explore two models applied to option prices to extract the risk-neutral probability density function (R-PDF) of the expected Can$/US$ exchange rate. Each of the two models extends the Black-Scholes model by using a mixture of two lognormals for the terminal distribution, instead of a single lognormal: one mixed lognormal imposes a specific stochastic process for the underlying asset, and the other does not. The contribution of the paper is to propose a simple methodology to build R-PDFs with a constant time to maturity in the absence of option prices for the maturity of interest. The authors apply this methodology and find that the two models provide similar results for the degree of uncertainty (i.e., the variance) surrounding the future level of the exchange rate, but differ on the likely direction of the exchange rate movements (i.e., the skewness).
Exchange rates Econometric and statistical methods Financial markets