# Treasury Futures Wild Card

I am looking at some empirical methods to model the Treasury Futures wild card. I was looking through some sell side reports and found this statement.

"Wildcard fair BNOC is the net basis under which the wildcard is fairly priced assuming 1bp/2hr from 3-5pm each day"

Edit: Per the response below I have been looking into the equations in this report: https://docs.google.com/document/d/1IXuJ30WK7R9GyH6RUd6dockTKqu_rbpux3A0ldcAIjc/edit#61;sharing

I am trying to understand this equation and I am a bit lost. I've had maybe one course in probability theory and hope someone can explain the rationale.

The equation is the following:

$E_{n}=&space;(1-C)&space;*&space;\left&space;[&space;\sigma&space;^{2}*p(x_{1})&space;+&space;\frac{x_{1}}{2}\left&space;\{1+erf(\frac{x_{1}}{\sigma&space;\sqrt{2}})&space;\right&space;\}\right&space;]$

This is the expected payoff of exercising early if there's a sizeable move in the price or waiting and earning one day of gross.

I don't understand the breakdown of the equation.

What is $\sigma&space;^{2}*p(x_{1}$ and what is the second part $\left&space;[&space;\frac{x_{1}}{2}\left&space;\{1+erf(\frac{x_{1}}{\sigma&space;\sqrt{2}})&space;\right&space;\}\right&space;]$ intuitively?

The second part looks like its a cumulative probability blank">{1})" title="P(x < x_{1})" /> but not entirely sure

Read the latest research by Munier Salem and the rates group at JPMorgan, they just published a piece of research that uses the Option Adjusted Implied Repo Rate. A buy-side guy posted it to page 7 of this document https://docs.google.com/document/d/1IXuJ30WK7R9GyH6RUd6dockTKqu_rbpux3A0ldcAIjc/edit#61;sharing . I can only assume this publication is why you're researching it in the first place...but this metric should work

• I took a look at the document. Does that equation suggest that the wildcard value at the beginning of the delivery period is the cumulative value of the payoff working backwards in time? – VanillaCall Feb 13 at 3:54

@decaybeta - "empirical methods" would mean looking at historical moves in the cash market during the relevant time periods to come up with a fair value (then presumably adding some risk premium) - not pricing via Black Scholes.

Perhaps the NBER paper, "Valuation and Optimal Exercise of the Wild Card Option in the Treasury Bond Futures Market" by Kane and Marcus, 1985, would be of use.

@byouness - there's no link posted.

EDIT: Down-voting replies that provide papers that answer your question is probably not a good way to encourage people to answer your questions.

This (the wildcard option) is discussed in the book, "The Treasury Bond Basis", on pages 71-73.

• I have the book and it simply discusses the break-even move in the tail not valuing the option – decaybeta Dec 5 '19 at 3:36