I am facing the valuation of various IR exotic structures. For each of them I want to choice a model "adapted". By "adapted", I mean a good compromise between market conformity, precision, speed and quality of the inputs needed. I selected some of those products to get your advise :* bermudan swaption and KO bermudan swaption* range and callable range* collar on a CMS spread* range on a CMS spreadCan you suggest me one of more model for each of those products, giving the advantages and disadvantages of your proposals ?ThanksC

calculator,I'm currently reading "Term Structure Models: a Review" by Rebonato which discusses how many different IR models are related and discusses (dis)advantages of them. It doesn't tell you how to price exactly the different products you speak about but try it outYou can download it from his website: http://www.rebonato.com/TSMRS.pdf-- allu

This is a difficult question, and I think almost impossible to answer based on the the level criteria you outline. Every model not only has implicit assumptions about how the interest rates / vols / correlations etc. interact and are able to evolve, but typically also have further calibration / implementation decisions you need to make within the model. Quite often these decisions (such as for example form of the vol in Libor Market model, number of factors, choice of calibratrion instrument) will have as great an impact within the same model framework as moving to a different model in terms of speed and "quality" of pricing.While there are often very good technical reasons for choosing one particular framework for a particular product type, I think there's a large benefit in choosing a single model that you think you are confident in being able to tame in implementation (I'm assuming you're thinking about building this yourself). Then it's a matter of understanding how and why your pricing is different from market prices you see. Quite often you can then make local adaptions to account for any understandable discrepancies you see. Basically the core elements of most mainstream models are fairly straight forward, so it shouldn't take long to put together some sort of basic system. This gives you the best insight as to what suits you best, then when you're happy with that you can go on to slot in all your fancy calibration routines.

Thanks for the two first answer.I'll read carefully the article of Rebonato.I'll use an external library (instead of building the models by myself).Today, I think that I will use HW with piecewise constant volatility for bermudan swaption. I am not sure I can use it for KO bermudan swaption. What do you think ?For range, I am interested by a BGM model which can be calibrated on volatility of caps with smile effect. Even for the callable one it looks interesting.For products on spread (same currency) I am still confuse today.C

Hi Slevin,Why BK instead of HW for bermudan swaption ?By KO bermudan I mean knock-out; we observe a swap or a libor rate and if a certain level is observed the option disappears.Range with BS : serie of daily digital ? How do you manage the convexity adjustment (digital paid on one day some time after the fixing) ? By using adjusted in the digital formula (small cap spread) ?Some products on CMS spread are callable.When you indicate that you replicate a cap on CMS by a swaption do you man it is the same value with an adjusted nominal ? You need to rebalance your nominal amount continuously ?C

Now, I ain't an interest rate quant by any stretch of the imagination. I do have a pretty good comprehension of the basic standard models used (minus the string model). I've a question that is important for my work. If you do baby HJM (like HW, HL, or some other affine model) and you calibrate stuff to rates and either swaptions or caps/floors, then you get certain implied results for Quantos and CMS caps/floors. If you do simple Black on either swaptions or caps/floors, then you get different calibrations for Quantos and CMS caps/floors. How do you reconcile these differences? Do you care? What the fuk, should you punt? Is it merely the diff between lognormal discount bonds and lognormal forward rates? Do you just wave your hands, look for a white board, and say, "hehehhee, I'm right"?

The main issue with the well known IR models like BK (log-normal) , HW(normal), is the ability to properly deal with the volatility skew observed in the marketA couple of studies showed that log-normal models tend to overestimate ITM cap and underestimate OTM onesand normal models the opposite (underestimate ITMs, overestime OTMs), especially in a low IR environment.So, i would say the choice between HW and BK would more a question of taste....Concerning the pricing of some IR extocs, my choice would be in order of preference :for Bermudan options1f-2f HW with piecewise constant volatilities;for range swaps/notes1f with log-normal shifted BS with convexity adjusted forward rates;1f Libor Market Model in an implied tree framework, fitted to cap smile;for callable range is more complexwe don't really know how to calibrate itthe ideal choice would be a multi-factor BGM model which will be jointly calibrated to effective cap & swaption prices1) calibrate to cap prices: - for term structure : use some local piecewise constant vol or parametric one; - for skew : use a mixture between log-normal/normal - for smile: add a stochastic vol process etc;2) calibrate to swaption prices , usually ATM but if possibil to effective strike swaptions;for CMS callable structures the same model which would be calibrated only to swaption pricesother choice would be to use a 2f HJM(HW) model to approximate the prices and to avoid computational burdenfor low dimensional problems up to 3 dimensions (often with weak dependent payoffs) one could use FD ADI methods (predictor/corrector one if any mixed derivatives)Otherwise one should resort to MC with control variates For more details seeAndersen & Andreasen Volatility skews & extensions of the Libor Market modelAndersen & AndreasenExtended Libor market models with stochastic volatilityBrigo & MercurioInterest rate models book;And many other great papers could be added...Hope it will help,

Val, do you have the "Extended Libor market models with stochastic volatility" paper?Thanks

Here is the paper ELMM_SV: