Swaption Vol Basic Question

[ddrdouble]

hi everybody,



i am just interested in basic question regarding market practice for change of notice period:

lets assume there is a market for standard swaption 5y5y (that means 2 business day notice), this gives the vol for your prefered standard model.

What kind of vol would you use to price the same option with a much longer notice period,

something like 6m, so expiry in 4.5y, but the underlying and therefore forward is still the same.

Some people seem to use just a linear interpolation on variance, or would you try to use quotes for different options (like 4y5y and/or 4y6y)

any practical thoughts?

[Martinghoul]

You're effectively trying to price a mid-curve option. There's a number of things you can do, ranging from the trivial to the more complicated. Question is, how complicated/accurate do you want to get?

[Swap]

Martinghoul, How do we adjust the vol in this particular case based on the below vols quoted for standard swaption.










Expiry
 
1 YR
2 YR
3 YR
4 YR
5 YR
6 YR
7 YR
8 YR
9 YR
10 YR

[Martinghoul]

Well, the trivial and stupid way would be to interpolate the expiries for the same tail in the most straightforward fashion.



Another alternative that I have seen utilized is to use realized variances to obtain the ratio of mid-curve vol to standard vol. That ratio can then be used to compute the mid-curve vol, given the mkt input.



I am sure there are other methodologies...

[akimon]

the vol for the 4.5y fwd 5y swap (which expires in 0.5y), will be related to the vol of the 9.5y swap with 0.5y expiry, the vol of the 4.5y swap, with 0.5y expiry, and also the terminal correlation between the 4.5y swap and the 9.5y swap for the next 0.5y.



if you are really sophisticated, the forward vol of the 4.5y fwd 5y swap will also depend on their skews and the correlation skew of the above paragraph.

[ddrdouble]

sorry akimon,



but i meant the 0.5 fwd 5y swap (which expires in 4.5y) , if i understand you correctly, this would translate into:

0.5 fwd 5y swap vol (with expiry in 4.5y) depends on the 4.5y5.5y swaption vol and the

4.5y0.5y swaption vol (also keeping in mind that this means capvol in my case) and the terminal correlation between them.

is this correct?

of course the different strikes vs. atm level would mean that skew/smile matters

rgds

[Swap]

Thanks Martinghoul. So the assumption you are making is that the ratio is constant.

[Swap]

Thanks Akimon. That's interesing. So I have the interpolated vols for 0.5*9.5 & 0.5*4.5, but don't know how to get the terminal correlation.  ?

[sigis]

Depends on what you are trying to achieve here but basically you have two options. You could use historical correlations or you could try to get CMS spread option quotes with tenors and expiries close enough to what you need and imply correlations from those.

[Martinghoul]

swap and ddr, I have a paper on the specifics of the calculations akimon referred to. Send me an email and I'd be happy to share.