 pj
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Total Posts: 3604 |
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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? |
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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.
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 Pob
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Total Posts: 61 |
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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.
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 sv507
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Total Posts: 165 |
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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. |
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 granchio
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Total Posts: 1541 |
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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)
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"Deserve got nothing to do with it" - Clint |
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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? |
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 mj
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Total Posts: 1049 |
Joined: Jun 2004 |
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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.
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More mathematical finance is on its way!
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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? |
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 mj
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Total Posts: 1049 |
Joined: Jun 2004 |
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agreed -- but very hard to write!
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More mathematical finance is on its way!
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 amin
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Total Posts: 295 |
Joined: Aug 2005 |
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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.
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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).
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вакансия "Программист Психологической службы"
-але! у нас ошибко! не работает бля-бля-бля
-вы хотите об этом поговорить? |
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 amin
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Total Posts: 295 |
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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. |
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 sv507
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Total Posts: 165 |
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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?
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вакансия "Программист Психологической службы"
-але! у нас ошибко! не работает бля-бля-бля
-вы хотите об этом поговорить? |
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 amin
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Total Posts: 295 |
Joined: Aug 2005 |
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@ 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?
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 sv507
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Total Posts: 165 |
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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....
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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> 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? |
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 amin
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Total Posts: 295 |
Joined: Aug 2005 |
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"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. |
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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 |
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 nikol
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Total Posts: 1345 |
Joined: Jun 2005 |
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@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. :) |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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?

What about CMS vanilla instruments? |
The older I grow, the more I distrust the familiar doctrine that age brings wisdom
Henry L. Mencken |
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 nikol
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Total Posts: 1345 |
Joined: Jun 2005 |
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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. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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 pj
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Total Posts: 3604 |
Joined: Jun 2004 |
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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 |
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 nikol
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Total Posts: 1345 |
Joined: Jun 2005 |
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Sorry, you are correct. Writing up too quickly.
ATM slice only. Hence, ATM-surface. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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