Use a similar approach to that in Problem to derive the relationship between the futures rate and the forward rate for the Hull-White model. Use the relationship to verify the expression for θ(t) given for the Hull-White model in equation (30.14).
Problem :
Use a change of numeraire argument to show that the relationship between the futures rate and forward rate for the Ho-Lee model is as shown in Section 6.3. Use the relationship to verify the expression for θ(t) given for the Ho-Lee model in equation (30.11). (Hint: The futures price is a martingale when the market price of risk is zero. The forward price is a martingale when the market price of risk is a zero-coupon bond maturing at the same time as the forward contract.)
