Suppose MdRd is a martingale and define the risk-neutral probability corresponding to Md. Assume MdXRf is also a martingale. Show that dX X = (r d − r f

)dt +σx dB∗ , where B∗ is a Brownian motion under the risk-neutral probability. Note: This is called uncovered interest parity under the risk-neutral probability. Suppose,

for example, that r f < r d . Then, it may appear profitable to borrow in the foreign currency and invest in the domestic currency money market. The result states that, under the risk-neutral probability, the cost of the foreign currency is expected to increase so as to exactly offset the interest rate differential.