3. Consider a forward rate agreement that covers two time periods, [S1, Ti] and [S2, T2], where Si 0 and at time T receives Kl.eR".(T-Si), then pays K2 > 0 at time S2 and receives K2.ER* (T-S2) at maturity date T=T2). Let p(t,T) denote the value at time t [0,T] of the unit zero-coupon bond paying one monetary unit at maturity date T. Assume that for each fixed value of t, p(t, T) is non-increasing as a function of T. (a) Compute II(t) the value of the cash flow at any time t [0, S1), in terms of the unit bond prices, the forward rate R* and the other parameters of the model and the contract mentioned before. Give a formula for R* for which the FRA (forward rate agreement) is equal to zero at time t = 0) if the lengths of the two time periods are equal, i.e. T2 S2 = T1 - Si. (b) What is the value of R* for which the FRA is equal to zero at time t = 0) if the length of the second time period is twice as large as the first, i.e. T2 - S2 2(T1 - Si)? 3. Consider a forward rate agreement that covers two time periods, [S1, Ti] and [S2, T2], where Si 0 and at time T receives Kl.eR".(T-Si), then pays K2 > 0 at time S2 and receives K2.ER* (T-S2) at maturity date T=T2). Let p(t,T) denote the value at time t [0,T] of the unit zero-coupon bond paying one monetary unit at maturity date T. Assume that for each fixed value of t, p(t, T) is non-increasing as a function of T. (a) Compute II(t) the value of the cash flow at any time t [0, S1), in terms of the unit bond prices, the forward rate R* and the other parameters of the model and the contract mentioned before. Give a formula for R* for which the FRA (forward rate agreement) is equal to zero at time t = 0) if the lengths of the two time periods are equal, i.e. T2 S2 = T1 - Si. (b) What is the value of R* for which the FRA is equal to zero at time t = 0) if the length of the second time period is twice as large as the first, i.e. T2 - S2 2(T1 - Si)