Topics in foreign exchange: the spot rate and the forward rate

Abstract

This thesis looked at two areas in foreign exchange - the Spot Rate and the Forward Rate. In the spot rate section we fitted two stochastic differential processes - Geometric Brownian Motion and the Jump Diffusion Process. We derived solutions to these processes, and then fitted each of them using maximum likelihood estimation to real data. For all the spot rates we found that the Jump Diffusion Process fitted best. Other statistical tests were performed to look at the general nature of the spot rates. In the forward rate section we looked at the relationships between the current spot rate, the expected future spot rate and the forward rate under various assumptions about the economy. In particular, we looked at the phenomenon of the "Siegel's Paradox" and discussed its implications. Following that, time series analysis was undertaken on the forward rate data, and some of the assumptions were tested. The material looked at was primarily from the finance literature, but was presented here from a statistical perspective, and applied standard theory and techniques belonging to that discipline.