Question: In this problem we extend the Vasicek model to allow the mean rate to become stochastic. Think of a situation in which the Federal

In this problem we extend the Vasicek model to allow the mean rate θ to become stochastic. Think of a situation in which the Federal Reserve makes minor adjustments to short-term market rates to manage the temperature of the economy. The model comprises the following two equations:

dr = k(0-r) dt + o dB de = n dB

The Brownian motion d B is the same for both the interest rate r and its mean level θ. Answer the following questions:

(a) Given the bond price function P(r, 0, T), write down the process for d P using Ito's lemma. I denotes the

dr = k(0-r) dt + o dB de = n dB

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