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Empirical Approaches to the Treasury Futures Wild Card Option

Article Quant Q&A · Author: decaybeta
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Summary

The document concerns the wild card option embedded in Treasury futures and asks how to interpret an equation for the expected payoff from exercising early after a significant price move versus waiting to earn another day of gross. The responses point toward research on option-adjusted implied repo rates and recommend empirical analysis of historical cash-market moves during the relevant time windows, potentially with a risk premium, rather than assuming a Black–Scholes valuation. They also cite academic research on valuation and optimal exercise.

The material is mainly a set of pointers, not a derivation or explanation of the equation’s terms. It therefore suggests useful research directions but does not resolve the question about the probability component or provide data, model specifications, or empirical findings. Readers looking to build a valuation need to consult the cited literature and define the relevant exercise, delivery, and market conventions before applying an approach.

Key ideas

  • The Treasury futures wild card option concerns the choice between early exercise after a price move and waiting for additional gross.
  • Historical cash-market moves during relevant time windows can inform an empirical estimate of wild card value.
  • An empirical approach may incorporate a risk premium rather than rely solely on a standard option-pricing model.
  • The responses recommend further research but do not derive the equation or explain its probability terms.

Tags

FuturesFixed incomeOptionsDerivatives pricing
Full text
# Treasury Futures Wild Card


# 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:

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 and what is the second part intuitively?

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

## Answer by Tanay Trivedi (score 3)

https://quant.stackexchange.com/a/50198

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

## Answer by user42108 (score 1)

https://quant.stackexchange.com/a/50130

@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.

## Answer by user42108 (score -4)

https://quant.stackexchange.com/a/50106

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.