Skip to content
All library documents

Early Exercise of American Options on Interest Rate Futures

Article Quant Q&A · Author: gvkv
Read the original

Summary

The document considers early exercise of American options on Treasury futures. One standard argument is that an American call without an underlying cash-flow benefit has no reason to be exercised early, while American puts require a more involved optimal-stopping analysis. The replies characterize that analysis as a free-boundary problem: solve the option-pricing equation subject to an exercise boundary.

A further reply raises a practical funding consideration specific to listed futures options. These options may not receive daily variation margin, whereas the futures position obtained through exercise does. Exercising an in-the-money option can therefore deliver intrinsic value through futures variation margin sooner, but it also gives up the remaining out-of-the-money option value. The suggested rule of thumb compares the short-rate funding benefit on intrinsic value over the remaining time with the value of the put component surrendered. This is a simplified comparison, not a complete pricing rule; actual exercise decisions depend on contract conventions, rates, remaining optionality, and relevant costs.

Key ideas

  • Early exercise of a call is generally unattractive when holding the underlying provides no cash-flow benefit.
  • American puts require analysis of an optimal exercise boundary.
  • Exercise can convert an option position into a futures position subject to variation margin.
  • The proposed rule compares the funding benefit on intrinsic value with the option value relinquished.
  • The rule of thumb omits contract-specific details and is not a full valuation method.

Tags

OptionsFuturesDerivatives pricingRisk management
Full text
# When is it rational to exercise a bond option early?


# When is it rational to exercise a bond option early?












Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?

## Answer by Jeff Burdges (score 4)

https://quant.stackexchange.com/a/2405

As OracleOfNJ said, there is never any advantage to early exercise of an American style call option unless the underlying asset offers some advantage, usually dividends, which does not apply to interest rate futures.

American put options were among the biggest open problems in finance until people learned how to treat them as free boundary problems. In other words, you'd first derive the Black-Scholes-like PDE that describes the equivalent European option product, but you'd solve it with a lower boundary condition described in terms of the PDE's solution.

I've never thought about American put options on interest rate futures specifically, but a Google search for "American put free boundary problem" yields some reasonable starting points, and an arxiv.org search for "American put" has many relevant articles.

## Answer by OracleOfNJ (score 3)

https://quant.stackexchange.com/a/2401

Since the treasury note future does not pay coupons or dividends, and is a future as opposed to a cash instrument that you purchase, it is never optimal to exercise early.

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/22280

I have a different take on this. Listed options such as options on the 10yr Treasury future, are NOT subject to daily variation margin. That is different to the underlying futures contract, which IS subject to daily variation margin. Let's say a listed option is 10 points in the money, with a month to go. If you do not exercise, you have an asset worth 10 points at expiration which you have to fund for a month at the short rate, so it's worth slightly less than 10 points. If you exercise early, you get a futures contract and then the next day you get 10 points of variation margin delivered to your account, so it's better. The only thing you have given up is the 10 point out of the money put due to your early exercise. So the rule of thumb is:

Exercise early if : (short rate * daycount * intrinsic) > put option given up

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.