Forums > Basics > Swaption Vol Basic Question

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 ddrdouble Total Posts: 45 Joined: Nov 2006
 Posted: 2010-04-01 14:53 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 Total Posts: 866 Joined: Oct 2008
 Posted: 2010-04-01 16:21 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? Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness...
 Swap Total Posts: 11 Joined: Nov 2009
Posted: 2010-04-06 20:04

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 4 YR Vol 24.05 22.97 22.43 21.85 21.38 20.98 20.55 20.4 20.2 19.5 5 YR Vol 21.8 21.43 20.95 20.6 20.3 20.05 19.52 19.48 19.15 18.63

 Martinghoul Total Posts: 866 Joined: Oct 2008
 Posted: 2010-04-07 12:22 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... Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness...
 akimon Total Posts: 566 Joined: Dec 2004
 Posted: 2010-04-07 16:51 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 Total Posts: 45 Joined: Nov 2006
 Posted: 2010-04-07 19:06 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 the4.5y0.5y 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 mattersrgds
 Swap Total Posts: 11 Joined: Nov 2009
 Posted: 2010-04-08 14:02 Thanks Martinghoul. So the assumption you are making is that the ratio is constant.
 Swap Total Posts: 11 Joined: Nov 2009
 Posted: 2010-04-08 16:47 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 Total Posts: 59 Joined: Mar 2005
 Posted: 2010-04-08 17:28 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 Total Posts: 866 Joined: Oct 2008
 Posted: 2010-04-08 17:58 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. Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness...
 Swap Total Posts: 11 Joined: Nov 2009
 Posted: 2010-04-09 09:38 Thanks Martinghoul. I just sent you an email.
 ddrdouble Total Posts: 45 Joined: Nov 2006
 Posted: 2010-04-11 15:14 Thx Martinghoul, just did the same
 Martinghoul Total Posts: 866 Joined: Oct 2008
 Posted: 2010-04-11 20:47 I have sent it to you, guys... I hope it helps, although I realized, rather belatedly, that doesn't exactly cover the subject discussed here. Apologies for that. However, I think it should help somewhat. Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness...
 Swap Total Posts: 11 Joined: Nov 2009
 Posted: 2010-04-12 07:09 Nice paper Martinghoul. Though it doesn't talk about how to calculate 'terminal correlation', it was quite helpful.
 aghosh Total Posts: 3 Joined: Sep 2014
 Posted: 2014-09-09 11:57 Hi Akimon, I would like to get a understanding of pricing of Mid curve swaptions, specifically how to caluclate correlation between swap tenors and where to apply when calculating the pay off. If you have any paper on it please can you forward it to me. Regards Avirup Ghosh
 aghosh Total Posts: 3 Joined: Sep 2014
 Posted: 2014-09-09 12:11 hi Martinghoul, Could you please forard the document to me.
 akimon Total Posts: 566 Joined: Dec 2004
 Posted: 2014-09-10 04:42 For vanilla swaptions you don't 'calculate' the volatility, but back out the implied volatility from option prices. Therefore, for midcurve options, you also don't 'calculate' the correlation, but back out the correlation from midcurve option prices.
 aghosh Total Posts: 3 Joined: Sep 2014
 Posted: 2014-09-10 16:56 Thanks Akimon, but i meant was how do i calculate the value of a mid curve swaption when what i have as input is normal swaption vol surface smile calibrated using SABR model and swap rates. The other factor which is the correlation for valuing Mid curve swaption is what im trying to find out. Suppose i have a trade with 10 year underlying swap starting 3 year from today and option maturing 1 year from today. What are the two volatlity points i should refer from the vol surface and what are the two swap tenors for which i should imply the correlation.
 Martinghoul Total Posts: 866 Joined: Oct 2008
 Posted: 2014-09-10 17:06 Avirup, if you wanna me send you the paper, send me an email. Insofar as I may be heard by anything, which may or may not care what I say, I ask, if it matters, that you be forgiven for anything you may have done or failed to do which requires forgiveness...
 akimon Total Posts: 566 Joined: Dec 2004
 Posted: 2014-09-19 00:55 hi aghosh>> Suppose i have a trade with 10 year underlying swap starting 3 year from today and option maturing 1 year from today. What are the two volatlity points i should refer from the vol surface and what are the two swap tenors for which i should imply the correlation.if the underlying is 3y10y, and the option expiry is in 1y, then vol for the 1y into a (2y10y) midcurve will be related to today's 1y12y vol and today's 1y2y vol. more precisely, the joint distribution of theseif you assume a the distribution of the individual points are backed out from vanilla swaption skew (say, sabr or whatever model you use), then the correlation structure to define the joint distribution will define, or rather be defined by, the price of the midcurve.there is also some thread on the forum a long time ago:http://www.nuclearphynance.com/Show%20Post.aspx?PostIDKey=41010
 superlei Total Posts: 1 Joined: Oct 2014
 Posted: 2014-10-25 22:30 Martinghoul, can you please also send me the paper(s) you mentioned here. I'll send my email to you. Thanks a lot!
 mtsm Total Posts: 236 Joined: Dec 2010
 Posted: 2014-10-26 04:11 You can find the paper you are looking for in the following threadhttp://www.W****tt.com/messageview.cfm?catid=38&threadid=68640A more up-to-date and broader discussion on the topic can be found in Piterbarg & Andreasen.
 yenuwi Banned Total Posts: 1 Joined: May 2019
 Posted: 2019-05-04 09:09 Great post again! Through with this content, you have given stand out introduction. Appreciate the value of9anime website
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