Hello evrybody,I'm trying to implement SABR model in illiquid markets ( paper by Graeme West) and have some problems . Here is a summary:For a given price of a trade, atm vol and strike, and assuming random rho( corr.) and nu(vol vol), I find the sigma from SABR and use it to find the sigma fit (using Lagrange and NR method). using these sigma fits, I try to minimise the error between my sigma fit and the model sigma's and arrive at optimal rho and nu.1) I find that the sensitivity of sigma with rho and nu is very less and end up getting the optimised values almost equal to the initial valuesI provide ( as the sigma fits are extremely close to the sigma fit. a variation in fourth decimal is seen in vols)2) If I change the price to counter this effect, I find that the optimisation fails as the sensitivity is small as said earlier.3) I have not put any traps in my optimisation - like rho should be between (-1,1)- is there any problem with that?can anyone point exactly as to where I might be going wrong?

What opitmizer do you use ?Why don't you calibrate (alpha, rho and volvol) at the time ?

Hii again,I use Nelder Mead simplex for optimization. I do not have data of market volatilities of set of options at different strikes, instead I have the price at which they are traded, so I cannot directly calibrate for rho, nu and volvol.Instead, I assume some rho and nu, and use SABR model to get a temporary vol for each strike, and then calculate a new set of sigma_fit's(for each strike) under the constraint that the individual black schole prices must add up to the market price of the trade and the error exp. i.e vega* (sigma_sabr - sigma_fit)^2 must be minimumThen using these sigma fit's I compute my sigma_sabr minimising the same expression above (by tweaking rho and nu).I find that my first calculation of sigma_fit's for some random rho and nu itself is leading me to an error of the order of 10^-7. I feel that there is no point to tweak it any further -- I get the feeling that I must be missing something fundamental but do not know what.regardsnitant

Hi,Inverse your pirce by BS , and obtain implied vol. You should directly calibrate the imply vol. This is straigth, because sabr formulae is smooth, nice and fit well the smile.

Hi,Thank u for ur reply, it really helped as I'm doing a least square fit with my data.But I have a new question. In my error function I'm incorporating vega i.e my error expression isvega*(sigma_mkt - sigma_sabr)^2. When I'm calibrating for swaptions, my veg is of the order of 10^-3, coupled with a sigma^2 order of 10^-4, the error is of the order of 10^-7. So there is no point in doing least square fit with this error.But if I scale up vega by 100, I get an answer. And if i scale up by 1000 I get a different answer. This is obviously wrong. Can somebody suggest as to where I might be going wrong.

by multiplying by vega your error is homogenous to vol*price, and I don't really know the meaning.first, you can calibrate without any weighs.Secund, calibrate with appropriate weighs, which are not so easy. Sigma_mkt(Strike) reliability depends on the volume of the trade to this strike.I think your error should be: SUM ( (volmarket(Ki) - volSABR(Ki))^2, i=1..n) How do you reach your data vol ?

Hi everyone,I'm trying to implement SABR for FX option vol smile in USDINR (which is fairly illiquid). I've taken beta = 1, and have been trying Newton's iteration method to get the parameters alpha, rho and phi. the parameters are calculated separately for each maturity taking the 25D call / put and ATM straddle vols.The problem I'm facing is that for quite a few maturities, the Newton's method fails to give a solution. This is more true when RR levels are closer to zero.Has anyone tried this? Can someone point me in the right direction?

hiHave you ever tried the Levenberg-Marquardt mothod to solve SABR model???How do you find the derivatives of SABR???and is there any good ways to calibrate SABR except LM and Nelder???

hiI have tried some models of course included the SABR model.But these models still not fullfilled my need.Are there any other models or ways that could do better than this??Plz give me a direction.....thinks.