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billyx524
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CMS Spread

August 2nd, 2019, 2:00 am

Hi,

I have a question about the term "CMS Spread", can someone please clarify what exactly does it mean?

When people say the spread between two CMS rates (e.e. 10 year CMS rate minus 2 year CMS rate), is the so called "10 year CMS rate" and "2 year CMS rate" actually referring to the 10 year par swap rate and 2 year par swap rate?

And why is it said that the spread contains information on the slope of the yield curve?

Many Thanks!
 
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bearish
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Re: CMS Spread

August 2nd, 2019, 9:17 pm

Yes, CMS is an acronym for constant maturity swap. The term "slope of the yield curve" means slightly different things to different people, but is often represented by the difference between 10's and 2's, whether swap or government rates.  
 
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billyx524
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Re: CMS Spread

August 2nd, 2019, 10:13 pm

Is there a reason why it is called a CMS spread, instead of something like just swap rate spread?
 
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bearish
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Re: CMS Spread

August 3rd, 2019, 1:20 am

You may want to consult a slang forum, rather than Wilmott.
 
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Cuchulainn
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Re: CMS Spread

March 18th, 2024, 12:21 pm

Is CMS spread the same as a CMS spread range accrual?

I guess MC, Lattice FFT methods (not PDE spread  models) are usually used? 

// is a CMS spread much different from spread options, grosso modo? More HW2 than BS?
 
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bearish
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Re: CMS Spread

March 19th, 2024, 9:41 pm

A range accrual is essentially a bundle of digital options, usually presented in terms of a (relatively high) interest rate that will accrue (on a bond or a swap) as long as some reference quantity remains within a given range. When said reference quantity is a CMS spread you have on your hands a CMS spread range accrual. Unless there are further complications like global caps/floors, knock-out or call features, it probably makes sense to explicitly model it as a sum of a bunch of European digital options. Back in the day when I did these sorts of things for a living, there were two schools of thought: either throw the cash flows into your grand unifying multifactor model that would usually require MC solution or create an instrument specific model that abstracts away the parts of the yield curve you don’t need and attempts to get the dynamics of your particular CMS spread in question right. The latter approach would typically lead to more light weight numerical solutions, up to and including analytical approximations.
 
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Cuchulainn
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Re: CMS Spread

March 24th, 2024, 2:53 pm

Some background to my Q.
Only closed form solutions lend lucid insight.
Lucid and incorrect go hand-in-hand in many cases! You need to quantify the assumptions in your formulas because closed solutions break down when parameters are outside some range. But only heuristics (aka a-posteriori hand-waving) tell us if they are good or not.

We have a large number of mathematically and numerically correct PDE/FDM schemes for a range equity and ir/fixed income (CIR, HW1, HW2) problems (CN,ADE, ADI, ADICS, MOL, Marchuk, Yanenko, Strang, Saulyev, DD exponential fitting.)

Concrete example: one 2d test is Kirk's (1995) approximation as in Haug (2007), pages 213-214. It is good in the main but deep OTM, ITM less so. But all the fdm schemes give the same answers as each other.

We are not use traditional FDM, FFT or MC. Too much hassle.

Similar excellent results HW1, HW2 incorporating instantaneous forward rate.

Next step: a few of us to apply HW2 to CMS spread range accruals. Need to define the scope first..

Hypothesis: the best approximation to a closed solution is to apply [3,7] robust FD schemes to the PDE, letting dt -> 0, h -> 0 and checking results are the same. They all can't be wrong because each one is both a generalist and a specialist.
 
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bearish
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Re: CMS Spread

March 25th, 2024, 12:20 pm

Vanilla CMS spread range accruals are not primarily difficult to value from a numerical perspective (although you have to deal with a lot of discontinuities), but rather from the perspective of getting the spread process roughly right. For example, just about any 1-factor term structure model would be bad even if you get the forward rates and individual swap rate vols right, because you would most likely overstate the correlation between the CMS rates.
 
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Cuchulainn
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Re: CMS Spread

March 25th, 2024, 1:39 pm

Vanilla CMS spread range accruals are not primarily difficult to value from a numerical perspective (although you have to deal with a lot of discontinuities), but rather from the perspective of getting the spread process roughly right. For example, just about any 1-factor term structure model would be bad even if you get the forward rates and individual swap rate vols right, because you would most likely overstate the correlation between the CMS rates.
We have just started with quant/student project, who is working on the latter part. At least, we get the wiggly numerics out of the way. Swap rate vol should be OK I reckon (for HW1, HW2 it was not a major issue). 

Thinking out loud..
For correlation, I reckon we use historical data and Gauss Copula?
Could we use Uncertain Correlation (Paul W, vol 3, page 879) but it will be difficult to find suitable hedge correlation instruments.

Another idea (which BTW works for greeks and such) is to differentiate HW2 pde wrt [$]\rho[$] to get an uncertain pde. (??)

https://onlinelibrary.wiley.com/doi/pdf ... wilm.10014

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