The majority of the ideas presented in this text rest on the idea that the spot rate is a martingale (Equation (2.9)) and it therefore exhibits no mean reversion or autocorrelation. This leads to the variance of the PDF growing with time. This growth is linear in the case of IID returns. This book has presented options theory based on this assumption. The main purpose in this chapter is to provide some empirical evidence to support this idea.

Are future FX rates predictable using past rates alone? Is there mean reversion? Upon first inspection, one may be forgiven for suggesting that these questions are overly simplistic. After all, market participants are continuously bombarded with far more information relevant for forming forecasts than just past FX rates. However, this question *is* important and interesting at least partly because options theory is built on the idea that the discounted spot process is a martingale, although under the risk‐neutral probability measure. If the answer to the previous questions turns out to be *yes*, then there may exist exploitable profitable trading opportunities that take advantage of a misspecification in option pricing models. More generally, by studying this question, we learn whether the probability distributions that we use to model FX rates for the purpose of option pricing should incorporate some level of price‐based predictability.

I begin by restating the question ...

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