# Consider the pricing of a futures contract on a discount bond, where the short rate r t

## Question:

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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