In this problem we extend the Vasicek model to allow the mean rate to become stochastic.

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: 

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

Transcribed Image Text:

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