Duration and convexity of coupon bond futures

Coupon bond futures are among the most successful futures contracts in the world today. It may not be widely known, however, that if the cheapest to deliver of a coupon bond futures contract will have non-zero accrued interest on the futures delivery date, formulas for duration and convexity of the futures contract must account for the accrued interest in a way that differs from the process for coupon bonds.

We present duration and convexity formulas for coupon bond futures for the general case in which the cheapest to deliver bonds of coupon bond futures have non-zero accrued interest on the delivery dates. We present these formulas both in familiar summation expressions and in closed forms.

1. DURATION OF COUPON BOND FUTURES

We need to make simplifying assumptions about the shape of the yield curve and the way it shifts in order to derive duration and convexity formulas.1 We make two sets of assumptions. Under the first set of assumptions, the yield curve is flat and shifts in parallel. We call duration and convexity based...