# Treasury Futures Wild Card Option equation

I am confused about the equation on page 13 (upper right) from the CME: https://www.cmegroup.com/education/files/treasury-futures-basis-spreads.pdf

The equation calculates the move in the CTD that would make it worthwhile for the short futures contract holder to immediately exercise and sell the tail of the position.

In brief, the equation is

$$\textrm{Gross Basis} \times (CF / (1 - CF) < P_{late} - P_{2pm}$$

I understand that the 1-CF corresponds to the tail of the position. However, I don't understand why there is a CF in the numerator.

It’s because you only lose the Gross basis on a portion of the bonds (ie the amount that you will deliver against the futures).

For example if you start with 1 bond and short CF amount of futures, you will deliver CF bonds against the contract, losing the gross basis on CF bonds. . You will pick up P(late)- P(2pm) on (1-CF) amount of bonds.

• Thanks, that makes sense now. So the gross basis is really 1 - CF (Futures) but since you're only deliver CF bonds into CF (Futures), it's a portion of the gross basis that you lose, which is offset by selling the remainder 1-CF bonds if there's a sizeable move in the security. – VanillaCall May 10 at 1:28