Suppose that the spot interest rate process (rt)t0 follows the Vasicek model, with the fol- lowing parameters under the historical probability: speed a, level b and volatility . Assume a constant market price of risk . i) Write the model of rt under the (forward) risk neutral probability.

ii) Does the long run mean and variance are the same in the two models? Justify your answer and give their expressions. iii) Suppose now that the parameters under the (forward) risk neutral probability are: the speed a = 0.3, the level b = 0.01 and the volatility = 0.2. The initial value is r0 = 4% per year. Compute the price of a zero coupon bond with nominal value N = 10 Euro and maturity two years. Show in detail all passages for the computation.