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Why Embedded Option Valuations Can Produce Negative Values

Article Quant Q&A · Author: Flux
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Summary

The document addresses how a callable U.S. Treasury bond can appear to have a negative embedded option value. It distinguishes an independently traded option, whose market price cannot be negative, from an embedded feature that is inseparable from its parent bond. The embedded option value is inferred through a valuation calculation rather than observed as a separate market quote.

A negative calculated value is framed as a possible anomaly in the bond valuation decomposition, rather than evidence that a standalone option trades below zero. The result can arise when other influences on the bond’s price are omitted or dominate the modeled optionality. This cautions against treating the embedded-option approach as a complete explanation of security value in every setting. The answer offers a conceptual explanation but does not identify the omitted pricing component in the cited Treasury cases or give a model for estimating it.

Key ideas

  • An independently traded option cannot have a negative market price.
  • An embedded option is valued as part of its parent security and has no separate market quote.
  • A negative calculated embedded value can signal a problem with the bond valuation decomposition.
  • Unmodeled influences on the parent bond’s price may overwhelm the estimated optionality.

Tags

Fixed incomeOptionsDerivatives pricingUS markets
Full text
# Why are negative option prices possible for callable US treasury bonds?


# Why are negative option prices possible for callable US treasury bonds?












I am not familiar enough with the theories of option pricing to understand how negative option prices are possible. I found two research papers indicating that negative option prices are indeed possible for callable US treasury bonds:

- Are Negative Option Prices Possible? The Callable U.S. Treasury-Bond Puzzle

- Negative option values are possible: The impact of Treasury bond futures on the cash U.S. Treasury market

Can someone explain why negative option prices are possible for callable US treasury bonds?

## Answer by nbbo2 (score 4, accepted)

https://quant.stackexchange.com/a/66222

An actual option with an independent existence cannot have a negative price. But we are talking here about 'embedded options' that are part of another security (in this case a USTR bond) and cannot be separated from their parent. Their price is not quoted in the marketplace but is found by a calculation. The problem is that this calculation comes up with a negative number. It is more an ANOMALY IN BOND PRICING than a fact about options. The bond pricing takes other considerations into account that completely overwhelm the embedded optionality and make the calculation come out the way it does.

It shows the Embedded Option approach to security valuation does not always work. Because there could be another component of price which we have forgotten to include (an omitted component).

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.