Exercise 24.4.4 Consider a futures contract on a zero-coupon bond with maturity date T1. The futures contract expires at time T. Let F(r, t) denote the futures price that follows dF/F = μf dt +σf dW. Prove that F satisfies

−∂F

∂T

+[μ(r, t)−λ(r, t) σ(r, t) ] ∂F

∂r

+ 1 2

σ(r, t)2 ∂2F

∂r 2

= 0 subject to F( · , T) = P( · , T, T1), where λ ≡ μf/σf.