2. You know that the euro/dollar exchange rate et follows the real-world dynamics: det = dt +...

Question:

2. You know that the euro/dollar exchange rate et follows the real-world dynamics: det = μdt + .15etdWt (152) The current value of the exchange rate is eo = 1.1015. You also know that the price of a 1-year USD discount bond is given by B(t, t + 1)US = 98.93 (153) while the corresponding euro-denominated bond is priced as B(t, t + 1)EU = 98.73 (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?

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