I am referring to Piterbarg's paper "A Stochastic Volatility Forward Libor Model with a Term Structure of Volatility Smiles " (SSRN ID 472061).I would like to understand two things in his derivation of the approximation to the swap rate's coefficients in the proof to theorem 5.1. The first is: why is it a reasonable assumption that the SDEs in A.1 and A.2 can be taken to coincide on the paths along the constant forwards that are obtained from the starting point?The second is: Why does he discard the second order derivative terms in A.6? Such terms are not really that small -they are not second order expansion but rather just second order derivatives-, or if I am mistaken why is it so? The issues at hand are quite urgent, any quick serious help is really appreciated.Thanks in advance.

What has your experience with respect to stoc vol LMM models. What is the preferred stoc vol LMM model among quants?

Sorry for the late response....but the answer depends on what you want to do really. Overall I think you have the following types of models to deal with smile issues:1. Local vol model2. Uncertain Parameter Models3. Stochastic Vol models4. Fancy processes modelsThe first two can fit the smile correctly but fail in its dynamics (sticky moneyness etc.) and hence result in bad greeks...so good to price but not so good to manage the risk.The fourth can fit well and obtain right dynamics but are too articulate and in most cases impractical. Another con is typically hard to fit consistenly and in stable fashion and finally the often difficult implementation and slow pricing for complicated products.SV: You have many nowadays. -SABR is ok, and is probably the most common, although note that correlation needs to be included to be consdere a proper LMM. -Piterbarg fits the entire ATM swaptions matrix...may underestimate long term smile due to mean reversion.-Wu, Rebanato etc etc...got many there...although the most practical probably the above. Note that although SABR is very common it is based on an approximation which assumes vol of vol to be small among other things. Some brokers use it to quote exotics. It is sometimes worhtwhile to find an exact solution to a similar model.The world has changed though and I don't really know how it will be in a few months time with re to products complexity.

Hi there HaZim, I am looking into smile modellin in the LMM.You say that the Uncertain oarameter model produces annatural dynamics is there a published study you can point me to that highlights this issue?

http://papers.ssrn.com/sol3/papers.cfm? ... _id=393060

Hi, I implemented the stoch vol model as in Piterbarg's paper "A Stochastic Volatility Forward Libor Model with a Term Structure of Volatility Smiles ".In particular I used the proxy g(x) ~ a+b exp(-cx) (equation 6.19) to find an effective variance.I found that in my implementation this proxy doesn't work well anymore, if I calibrate to the current EUR swaption market data. When I use market data from the beginning of 2008 I obtain good results.Has anyone remarked the same effect or is it more likely that I have bugs my implementation?What would be a possible alternative if the proxy isn't suitable anymore?Thanks in advance.

Hello,I am working on this paper too, and the implementation is not working well either. Do you know why can we make this approximation: g(x) ~ a+b exp(-cx) ? with calculations, we realize that g''(x)/g'(x) is not a constant.Any response, will be much appreciated!Thanks in advance.

You can look up for an expression of this in my paper Calibration, Simulation, and hedging in a HESTON LIBOR Market Model with stochastic basis without derivation. I first noticed it in a German student's thesis about stochastic vol LMM. I would post the original thesis as soon as I can. My paper can be downloaded from http://ssrn.com/abstract=1704415. I also noticed that I failed to cite the above mentioned author 's work in my paper. I apologize to the author and would include his dissertation in my citations..

I just did a quick search and the dissertation is "Smile modelling in the LIBOR MARKET Model". The dissertation is by M Meister.Look at page 115. Meister's Thesis