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American Put-Call Parity Bounds for Non-Dividend-Paying Assets

Article Quant Q&A · Author: gvkv
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Summary

The document asks how put-call parity applies to American options on assets that make no distributions, including options on Treasury note futures. It gives the standard inequality for the difference between American call and put prices: that difference is bounded below by the spot price minus the strike and above by the spot price minus the discounted strike. This contrasts with the equality used for European options.

The discussion does not derive the bounds or quantify how much early-exercise rights add to option values. It points readers toward an article on American put-call symmetry as further context. The material is therefore a concise statement of a pricing relationship rather than a full valuation method; applying it still requires attention to the underlying, contract terms, and relevant rates.

Key ideas

  • For American options, the call-minus-put price is bounded rather than fixed by European put-call parity.
  • The lower bound is the underlying price less the strike.
  • The upper bound subtracts the present value of the strike from the underlying price.
  • The document states the relationship but does not derive it or quantify early-exercise value.

Tags

OptionsDerivatives pricingFixed income
Full text
# What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?


# What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?












If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from the usual assumption of a European option?

In particular, I'm thinking of bond options like the 10-year Treasury Note. Clearly options like these are worth more but how much more and what factors are required to evaluate put-call parity?

## Answer by Derek Ploor (score 9)

https://quant.stackexchange.com/a/2371

In John Hull's Option's, Futures and Other Derivatives, it states in the chapter "Properties of Stock Options" that from put-call parity, it follows for American options that $$ S_0 - K \le C - P \le S_0 - K e^{-rT} $$ where $C$ and $P$ are the American call and put prices.

In the book, the derivation is left as an exercise.

## Answer by Jeff Burdges (score 6)

https://quant.stackexchange.com/a/2406

There is an interesting article entitled American Put Call Symmetry from the mid 90s that might be what you want.

Updated link to the Carr paper: https://www.researchgate.net/publication/2357744_American_Put_Call_Symmetry

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.