Suppose that an interest rate evolves according to the following Stochastic Differential Equation (SDE):

drt = utdt + vtdWt

A bond Bt with maturity T is traded on the market. We want to apply Itos Lemma to find the Stochastic Differential Equation for the bond

. a) What is the price of the bond as a function of interest rate rt? [5 points]

b) Compute the derivatives required by Itos Lemma. [10 points]

c) Apply Itos Lemma and write down the Stochastic Differential Equation for the bond. Discuss your result. [15 points]