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Find the price of the Bond P (t, T) in the Vasicek model, by answering the questions below. For ease of calculations you may take all the parameters equal to 1, a = b = sigma = 1. (a) Assuming the model is specified under the Equivalent Martingale Measure (EMM), establish the formula for P(t, T) P(t, T) = E[e^integral^T_t r_s ds|F_t] (b) Let X = -integral^T_t r_s ds. Find mu_1 = E(X|r_t), the conditional mean of X given r_t. You may use without proof E(integral^T_t r_s ds|r_t) = integral^T_t E(r_s|r_t) ds. (c) Find sigma^2_1, the conditional variance of X given r_t. You may
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