Consider the pricing of a futures contract on a discount bond, where the short rate r_t is assumed to follow the Vasicek process defined by (7.2.20). On the expiration date T_F of the futures, a bond of unit par with maturity date T_B is delivered. Let B(r,t; T_B) and V (r,t; T_F ,T_B) denote, respectively, the bond price and futures price at the current time t. Show that the governing equation for the futures price is given by

with terminal payoff condition V (r,T_F ; T_F ,T_B) = B(r,T_F ; T_B). By assuming the solution of the futures price to be the form:

show that (Chen, 1992) 

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av p2 22V + at 2 ar2 av + [a(r - r) - p]: xp]an = ar = 0, t< TF,