Consider a forward swap rate S,(t)=i=+1iP(t,Ti)P(t,T)P(t,T) a. Define a numeraire under which the above forward swap rate is a martingale. b. Write down the Stochastic Differential Equation (SDE) for S,(t) under the measure defined by the numeraire in Question 5(a). c. Assume that =+2, please derive SDE of the forward swap rate S,+2(t) under the numeraire P(t,Ta). i. Write down the diffusion component. ii. Derive the drift component by change-of-measure toolkit