Implied exchange rate distributions: evidence from OTC option markets

Abstract

This paper uses a rich new dataset of option prices on the dollar-mark, dollar-yen, and key EMS cross-rates to extract the entire risk-neutral probability density function (pdf) over horizons of 1 and 3 months. We compare three alternative smoothing methods — cubic splines, an implied binomial tree (trimmed and untrimmed), and a mixture of lognormals — for transforming option data into the pdf. Despite their methodological differences, the three approaches lead to a similar pdf clearly distinct from the lognormal benchmark, and typically characterized by skewness and leptokurtosis. We then document a striking positive correlation between skewness in these pdfs and the spot rate. The stronger a currency the more expectations are skewed towards a further appreciation of that currency. We interpret this finding as a rejection that innovations in these exchange rates are independent of the level, or characteristic of a credible target zone, explicit or implicit. Instead, this positive correlation is consistent with target zones with endogenous realignment risk. We discuss two interpretations of our results on skewness: when a currency is stronger, the actual probability of further large appreciation is higher, or because of risk, such states are valued more highly.

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