Deriving option-implied probability densities for foreign exchange markets

This Handbook describes an important part of the Empirical Finance for Monetary Policy course run at the CCBS for the past few years, the use of options prices to estimate risk†neutral forecast densities for financial market prices. Central banks around the world make routine use of this information to assess market sentiment for a variety of asset classes. These for example include equities, oil futures and the focus of this Handbook, foreign exchange. With them, policymakers can assess risk†neutral predicted densities not just the most likely values. This provides a rich forecast information set, so that not just the most likely outcome can be ascertained, but also the market assessment of, say, any potential skewness in the density of possible outcomes. This whole area might seem impenetrable to the casual reader, needing as it does option pricing, density estimation and some mastery of a suitable computer language, but it turns out to be remarkably self†contained and easy to implement. With a relatively simple set of tools, all described here, it is a straightforward matter to estimate densities. We give a complete how†to guide, from finding appropriate data to giving the complete MATLAB code needed to get up and running. We focus on foreign exchange options for reasons described in the text, but our general approach to density estimation follows a similar methodology to that found in textbooks such as Taylor (2005), who implements similar techniques in Excel for equities.