The Fine Structure of Currency Returns Implied in One-Touch Options

Abstract

This article examines the fine structure of risk-neutral currency returns. For this purpose, I specify models comprising pure or time-changed diffusion risk, pure or time-changed jumps, or both. The models are calibrated to vanilla options and subsequently applied to the one-touch option market. Since one-touches are unspanned by a complete set of vanilla options, they lend themselves to a rigorous out-of-sample test. The results suggest that vanilla and one-touch option markets do not generally agree on the fine structure of currency returns: Evidence from the vanilla market favors a complex model with stochastic volatility and jumps, whereas one-touch options imply purely diffusive currency dynamics. This latter finding gives rise to two interpretations. Either, the high activity in currency markets is best reflected by the infinite variation of a diffusive risk factor. Alternatively, the result is an artefact of market makers who anchor their quotes to what the pure diffusion Black-Scholes model implies.

Keywords: Foreign exchange, Lévy process, one-touch option, Monte Carlo simulation, stochastic volatility, jumps

JEL Classification: C63, F31, G13