# 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?

• There is something wrong. Seaption values are positive. – dm63 Feb 23 '19 at 11:51

## 1 Answer

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.

• I have researched more since I asked the question, and it seems that swaption can have a forward premium such the behavior above is possible. In this case, the forward premium was roughly 100 million euros. The y-axis is denoted in DKK, hence the swaption price should be able to go all the way down to roughly -750 million DKK. – Martin Steen Andersen Mar 19 '19 at 10:57
• @MartinSteenAndersen I will edit my answer since I thought it was a standard contract. – Newbie Mar 19 '19 at 13:15
• Fair enough - I was indeed searching for the non standard contractual conventions by my question "I am wondering whether there is some market- or contractual convention that makes this swaption value possible?" – Martin Steen Andersen Mar 26 '19 at 11:02