I hope to begin some research into currencies. Before I come out with any result though, I thought I’d ask an open question and hope someone comes by with a response.
First of all, as a former scientist, thinking about currencies is very fun. See, for example, my previous article
This morning, I happened across a recent article that appeared on the arxiv:
The second paragraph really stood out:
One of the problems in foreign exchange research is that currencies are priced against each other so no independent numeraire exists. Any currency chosen as a numeraire will be excluded from the results, yet its intrinsic patterns can indirectly affect overall patterns. There is no standard solution to this issue or a standard numeraire candidate. Gold was considered, but rejected due to its high volatility. This is an important problem as different numeraires will give different results if strong multidimensional cross-correlations are present. Different bases can also generate different tree structures. The inclusion or exclusion of currencies from the sample can also give different results.
This is interesting because financial modeling is often about prices of securities or changes in prices. Currencies are about the relationship between prices. In graph theoretic (or category theoretic) terms, it is tempting to say that currency models should be about directed edges (or morphisms).
Is the best way to model currencies to choose some numeraire as is done in this paper? Or is there a way to study the relationships (morphisms) directly?