Suppose that the price of a zero-coupon bond maturing at time 7 follows the process dP(t,T) = HpP(t, T) dt + pP(t,T) dz and the price of a derivative dependent on the bond follows the process df=uffdt+off dz Assume only one source of uncertainty and that of provides no income.

(a) What is the forward price F of for a contract maturing at time T?

(b) What is the process followed by F in a world that is forward risk neutral with respect to P(t, T)?

(c) What is the process followed by F in the traditional risk-neutral world?

(d) What is the process followed by f in a world that is forward risk neutral with respect to a bond maturing at time T*, where T* T? Assume that op is the volatility of this bond.

AppendixLO1