2. (Exchange rates and LIBOR rates.) You know that the euro/dollar exchange rate et follows the real-world dynamics:

det 5 μdt 1 0:15etdWt (13.152)

The current value of the exchange rate is eo 5 1.1015. You also know that the price of a 1-year USD discount bond is given by Bðt; t11Þ

US 5 98:93 (13.153)

while the corresponding euro-denominated bond is priced as Bðt; t11Þ

EU 5 98:73 (13.154)

Both of these prices are arbitrage-free and there is no credit risk.

a. What are the 1-year LIBOR rates in these two currencies at time t?

b. What are the continuously compounded interest rates rUS t ;rEUR t ?

c. Obtain the arbitrage-free dynamics of the et. In particular, state clearly whether we need to use continuously compounded rates or LIBOR rates to do this.

d. Is there a continuous time dynamic that can be written using the LIBOR rates?