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pj


Total Posts: 3530
Joined: Jun 2004
 
Posted: 2009-05-01 16:47
Ok, the question is bit large in general.
I am interested in calibration wisdom
in all classes, all instruments, all models.
Like those two classical papers by Hagan
mention briefly how one should calibrate the
CMSs and range accruals. And I hear them
often and am inclined to believe.

So where could the references be found?
And what is the current wisdom?

Attached File: HaganPS accrual swaps and range notes.pdf
Attached File: HaganPS convexity conundrums. pricing CMS swaps, caps, and floors.pdf

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

pj


Total Posts: 3530
Joined: Jun 2004
 
Posted: 2011-02-17 15:18
Anyone?
For example how to use Hull White 2 Factor model?

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

silverside


Total Posts: 1417
Joined: Jun 2004
 
Posted: 2011-02-17 15:29

hi pj

I am interested the same topic (specifically related to interest rates). I think a lot of it is acquired knowledge bordering on folklore.

I don't know if you will find any single reference although the usual books (Brigo & Mercurio, Rebonato ) have some discussion. I particularly like the discussion chapter at the end of B&M which takes the form of a question-and-answer with an imaginary trader.

There are one or two big expensive books on IR modelling in the last few years  (possibly by Gatarek and / or Andreasen?) which I haven't read but may be worth a look.

 

 


Pob


Total Posts: 61
Joined: Dec 2008
 
Posted: 2011-02-17 19:01
Piterbarg might be your best bet.

For calibration in general, Wim Schoutens seems to have done a lot in that area, you might find something if you google around for him.

sv507


Total Posts: 165
Joined: Aug 2010
 
Posted: 2011-02-17 21:53
Hi PJ

I would second the andreasen/andersen/piterbarg papers and book. Have you seen

factor dependence of bermudan swaptions
the tarn paper by piterbarg discusses calibration for a 2 factor SV cheyette model
you can download various papers by them - eg google for cheyette model


I believe piterbarg's book deals with 2 factor cheyette.

basically they suggest using a LMM model to identify significant swaption covariances and then use low dim model calibrated to match those swaptions.

granchio


Total Posts: 1541
Joined: Apr 2004
 
Posted: 2011-02-17 22:39
I am interested in calibration wisdom
in all classes, all instruments, all models.


I certainly do not have wisdom, just accrued observation over the years.

If I were to distill something, I would say that calibrating well often requires a fairly in-depth knowledge of the market you are talking about, and its idiosincrasies. E.g. what systems are the marketmakers using, what is easy to cross and what not... who dominates the OTC market,etc
(I guess this might be one of the reasons why firms getting into reval often find it hard)

"Deserve got nothing to do with it" - Clint

pj


Total Posts: 3530
Joined: Jun 2004
 
Posted: 2011-02-18 10:07
Thank you gentlemen,

Now I need to grok the info.

From what I saw that you try to replicate the prices
of the counterparty.

For an anecdote.

Once the guy was trying to
replicate the prices of some
exotic stuff of the counterparty
which was deemed to be very sophisticated.

Seemingly meaning some fancy LMM model.

After a several attempts
the frustrated replicator
took HW1F with the calibration to the diagonal.
It fitted to a basis point

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

mj


Total Posts: 1049
Joined: Jun 2004
 
Posted: 2011-02-18 11:11
One of the paradoxes of the field is that whilst it's calibration that drives the success of a model, it's very hard to get papers on the topic published.

More mathematical finance is on its way!

pj


Total Posts: 3530
Joined: Jun 2004
 
Posted: 2011-02-18 12:08
A book "Calibration for dummies" would be a best-seller.

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

mj


Total Posts: 1049
Joined: Jun 2004
 
Posted: 2011-02-18 21:53
agreed -- but very hard to write!

More mathematical finance is on its way!

amin


Total Posts: 295
Joined: Aug 2005
 
Posted: 2011-02-18 22:44

Regarding the subject of calibration, there are several steps that have to be carried out.

1. You have to have a well defined objective function. In case of Stochastic volatility LMM, for example, this could be sum of squared difference between model and market swaption prices in the swaption cube. This part is really very model specific and usually has to rely on closed form formulas that could be easily calculated very quickly.

2. Minimization of objective function is the second part and this has to rely on some kind of optimization technique. Though same optimization technique could work for various model defined objective functions, some optimization techniques work better for some problems and vice versa.

But I think when we usually talk about calibration it is usually more about choosing a good optimization algorithm. 

I have worked with several optimization algorithms ranging from those employing fancy mathematics to other very simple and common sense methods. I have found that simple and faster common sense methods usually work better than other methods using advanced mathematics though NOT ALWAYS.

One important thing that I learnt from experience in large scale optimizations involving for example several hundred parameters in case of SVOL LMM and may be 9-10 parameters in case of simple SVJD models is that one has to resist the urge to take large steps when moving towards minima. Very good optimization methods have a tendency to get into local minima and other problems which can many times be avoided by restricting the step size with step size uniquely chosen for particular problem by experimentation. If you think you have a very good minimization algorithm but it continues to get trapped into local minima, just try to restrict the step size and there is a good chance that it will result in a far more robust algorithm.

I have done extensive work on calibration oflarge scale  SVOL LMMs, SV and SVJD models and if you want more information you can email me which should be in my profile.

 

 

 


pj


Total Posts: 3530
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Posted: 2011-02-19 13:12
No, I am talking about more simple problem.

The step 0 so to speak.

How to choose the vanilla instruments (and the model) for model calibration when pricing something more exotic.

Of course it does depend the instrument.

( I was told once that lots of
banks got stuffed when used Hull White 1 Factor model for pricing and selling steepeners).

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

amin


Total Posts: 295
Joined: Aug 2005
 
Posted: 2011-02-19 13:38

Vanilla instruments obviously should be the ones that you use for hedging the exotics. However there are other dynamics like correlations which cannot be fully translated into the model when you calibrate only to the instruments you use to hedge and that may require you to add additional instruments into calibration.

 If you only use hedge instruments in calibration, there can be several ways a model like LMM with many parameters, can be calibrated to market so you mayhave to add other instruments to pin down free variables. On the other hand short rate models may not be a perfect fit even to hedge instruments due to lack of free parameters. So you should ask yourself whether calibrated model fits to prices of hedge instruments and captures other market dynamics like correlations and skew, smile etc.

Choosing a good model is a study of fitting model using implied calibration and repeating over historic data and then you can see which model fares better.

Obviously if the purpose is only to fit market prices, you can just ask some brokers instead of getting into model development.


sv507


Total Posts: 165
Joined: Aug 2010
 
Posted: 2011-02-19 14:26
pj

you might also look at phil hunt's work
I found this paper...
hunt longstaff schwartz.




pj


Total Posts: 3530
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Posted: 2011-02-19 17:17
Thank you for paper, sv507!

@ Amin, well you are right but super duper models can sometime miss something quite substantial.
Like negative interest rates.

And not trying not to get into numbersixeque philosophies.

But where do the brokers get the prices from?

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

amin


Total Posts: 295
Joined: Aug 2005
 
Posted: 2011-02-19 18:20

@ Amin, well you are right but super duper models can sometime miss something quite substantial Like negative interest rates.

It has been more than six years since I touched Hull White but it is a Gaussian model so should give negative rates. A very good modern model is Heston LMM with displaced diffusion and can result in negative rates but various coefficients of displaced diffusion can change the model from lognormal(no negative rates) on one extreme to totally Gaussian (large probability of negative rates) on the other extreme. Usually displaced diffusion coefficient is chosen to fit the skew but probability of rates going negative can be considered a factor while fixing it.

What other things do you think modern models miss?


sv507


Total Posts: 165
Joined: Aug 2010
 
Posted: 2011-02-19 19:05
amin
I'm sure pj knows all about these - but the issue is hedging performance. with MC your risk will be poor. Add to that the daily calibration error of LMM and esp LMM heston, and you soon find you are not losing a significant portion of the theoretical value of the trade. That's surely why pj is into 2factor hull-white - the risk is good...so then the question is how do you calibrate your 2 factor model so it captures the dominant risks of the trade....

pj


Total Posts: 3530
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Posted: 2011-02-19 19:12
> so it captures the dominant risks of the trade

Hear! Hear!

вакансия "Программист Психологической службы" -але! у нас ошибко! не работает бля-бля-бля -вы хотите об этом поговорить?

amin


Total Posts: 295
Joined: Aug 2005
 
Posted: 2011-02-19 19:22

"but the issue is hedging performance. with MC your risk will be poor"

This is not true for all exotic instruments but for some it is true. But really you may not be able to find the risk of these exotic instruments by PDE either due to complexity that can only be tackled by MC.

"Add to that the daily calibration error of LMM and esp LMM heston"

I believe properly calibrated Heston LMM models have less calibration error than short rate models. Do you fit to market smile when pricing exotics with HW. Heston LMM does that quite nicely.


pj


Total Posts: 3530
Joined: Jun 2004
 
Posted: 2020-05-18 14:37
I was much younger then.
But the question still stays.
Let's stick to interest rates at the moment.
How does one calibrates a model for a, say, CMS steepener?
Maybe now there is some newer ideas?
And I don't mean some secret sauce.
Some vanilla practices.
Mainly avoiding big PV jumps for no reason.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 1175
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Posted: 2020-05-18 15:03
@pj
"How does one calibrates a model for a, say, CMS steepener?"


it is 2-step exercise:
- multi-curves = OIS (better your blended funding), ~LIBOR (subject to change)
- if product is across currencies, then you also need xcurrency basis
- IVOL cubes (Caplet/Floorlets, Swaptions)

having that you have to choose your dynamic models for curve (short rate? LMM/BGM?) and for the vol (select some stoch. vol model in the shop)

If it is done, then you can workout price of CMS steepener.

Hope, I did not miss anything.

PS. Easier to make the list, then to have it done. :)

pj


Total Posts: 3530
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Posted: 2020-05-18 15:11
Let's stick to the single currency and say the curves are worked out.
(Which is, I agree, a strong assumption)

Do you propose to pass the whole cubes?
Confused

What about CMS vanilla instruments?

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 1175
Joined: Jun 2005
 
Posted: 2020-05-18 15:22
CMS has convexity adjustment. CMS is linked to ir-futures. If you have them, then you can just make linear inter/extrapolation. I.e. you may skip vol calibration. However, if you do, you will not know your vol sensitivity (if you are regulated, you are in trouble then).

What do you mean "pass cubes"?

PS. Ah. IR-futures mature before 1yr. Yes, you have to calibrate ivol cubes.

pj


Total Posts: 3530
Joined: Jun 2004
 
Posted: 2020-05-18 16:24
A whole volatility cube?
I'll be back.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 1175
Joined: Jun 2005
 
Posted: 2020-05-18 16:35
Sorry, you are correct. Writing up too quickly.

ATM slice only. Hence, ATM-surface.
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