5. Let I (T) be survival indicator function, B(t, T) be the timet price of a default free bond price maturing at T and B (t, T) be the timet price of the defaultable counterpart with zero recovery rate. Let P(t, T) be the implied survival probability over [t, T]. (a) Show that B(t, T) P(t,T) = E[I(T)] 2 BE, T). What is the assumption required in order to obtain the above relation? [3] (b) The instantaneous riskfree and risky forward rates are related to B (t, T) and E, T) v1a m, T) : 3 ln Bft, T) 3T t, T) : 'ai" lnEft, T). Solve BUS, T) in terms_of t, a), t S u S T. Express PU, T) in terms of an integral involving f(t,u) and f(t,u), t S a S T. [3]