Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 2 / 28J / b / Solution

The Dollar bank account is a tradable asset whose Euro value is $Y_t{e}^{r_{D}t}$. Under the Euro equivalent martingale measure, discount this value by $e^{r_{E}t}$. The result is a martingale precisely when $\mu +r_D-r_E=0$, givingWhen the rates coincide, $\mu =0$ and part (a) proves that the exchange rate itself is a martingale under $Q_E$.