Why a Standard Swaption Payoff Cannot Be Negative
Summary
The document addresses whether a bought swaption can have a negative value under parallel interest-rate curve shifts. Its answer distinguishes the value of the underlying swap from the option payoff: the swap’s value can be negative after a curve bump, but a standard swaption payoff is the greater of that swap value and zero. The option holder can therefore decline exercise when the swap is unfavorable.
This explains why a negative shifted swap value does not, by itself, imply a negative exercise payoff for the bought option. The response is brief and does not analyze the interpolation method, market quotation conventions, valuation before expiry, or the source of the unusual data. Its conclusion is specifically about the standard contract payoff; diagnosing the reported valuation shapes would require more details about the model and the precise value being plotted.
Key ideas
- A swap’s value can become negative under a rate shift.
- A standard swaption payoff is floored at zero because the holder can choose not to exercise.
- Negative underlying swap value alone does not make the standard bought swaption payoff negative.
- The response does not establish whether unusual pre-expiry model valuations or interpolation results are correct.
Tags
Full text
# Can the value of a swaption at any time become more negative than the swaption premium?
# Can the value of a swaption at any time become more negative than the swaption premium?
I am interpolating swaption values as a function of parallel shifts in interest rate and have come across some peculiar shaped options among the data I have at hand.
Here is an example of a simple linear interpolation of the swaption value as a function of -100 to 100 bp shifts in interest rate:
The plot shows a bought receiver swaption with the usual convexity and differentiability as expected prior to option maturity.
Most important, the swaption value is positive (disregarding the premium). Among my data, I do though see some examples of swaptions which do not have this option-like shape, but instead yield almost equally positive and negative value in a $\pm$ 100 bp parallel shift. For example:
I am wondering whether there is some market- or contractual convention that makes this swaption value possible? If not, I must be right in expectingt the model which provides my data is doing something wrong. I know that the model is based on a parallel shift in rates and normal implied volatility. I do not think the model is based on realized skews but pure parallel curve shifts wit constant volatility.
I am just thinking that if the shifted rate is such that the option is out of the money, one would simply not exercise the option and hence the value must at least be positive if the option is bought and negative if sold. Am I wrong, or is the model wrong?
## Answer by Pithit (score 1)
https://quant.stackexchange.com/a/44607
Well, in a standard contract, if you bumped the curve, this will affect the swap value (which can be negative). However, since the swaption payoff is $Max(V_{swap},0)$ , where $V_{swap}$ is the swap value, this cannot be negative.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.