Hi there,I am currently reading Hagan's article on the SABR. However, I am having some trouble in implementing the dynnamic SABR since I am not completely sure about how I can calculate v_bar and eta_bar as well as how to deal with the epsilon in the formula for sigma_B after (B.58b - d). I would be very grateful for some sample code or any comments. Haven't fouind anything in the previous theats on SABRMucki.

Hi Mucki,I am a newbie and I am also trying to implement the dynamic Sabr. From my understanding, the epsilon parameter should be set to 1 (read comments on Epsilon just before section B5). As for the other parameters, let me know if you have found anything. If by any chance, you finished implementing the model, I'll be more than happy to have a look at your work, if you don't mind.Thanks,,Fayce.

Hi all,Does anyone have already implemented the dynamic sabr?I don't understand what are the parameters v_bar and eta_bar? Are they parameters of the models and given as such by the trader or calculated parameters?Also, what is the function v(t) used in the formula for theta_bar?If anyone can help, really appreciated.Thanks.

Hi,I'm studying the dynamic part of the Hagan document and trying to apply it to piecewise-constant parameters (for equity market). I don't see how to calibrate it. Here is how I understand the development:1. Static SABR: take a basket of options of same maturity and different strikes. The model enables to fit rather well all their implied vols with 3 constant params alpha, rho and nu (through the well-known formula sigma(K,tau)=...)2. Dynamic SABR: should a priori enable to fit a basket of options of different strikes and different maturities. The model has now three time-dependent parameters gamma(t), rho(t) and nu(t), plus the constant alpha.As I understand, Hagan et al. expresses the price of a vanilla option under this dynamic model as a function of two new time-dependent functions eta(s) and v(s). Then it replicates this price by replacing eta(s) and v(s) by constant -average- values eta bar, v bar and eventually theta bar. It shows that with these 3 parameters, the implied vol under the dynamic SABR is of the same form than under the static SABR. Finally, the values of eta bar, v bar and theta bar are obtained as functions of the original time-dependent params gamma(t), rho(t) and nu(t).I applied this to piecewise-constant params gamma(t), rho(t) and nu(t) and obtained the corresponding expressions of eta bar (eq. B37), v bar^2 (eq. B47) and theta bar (eq. B58.d), as functions of all levels gamma(1),...,gamma(n), etc.My problem now is to calibrate these parameters. A full optimization on the whole basket of options and all params of course leads to local min (without speaking of calculation time). Then I thought of bootstrapping but I don't see how to do.Actually, I see a contradiction in all of this: if it was possible to find good values for all levels of the time-dependent params (that is, in order to fit rather well all the calib instruments), then it would be possible to directly find good values of eta bar, v bar and theta bar. In this case, why not directly using them in the static model, by replacing rho and nu (ok, a small extension is needed to insert the theta bar)? In other words, according to me, if the dynamic model could fit a whole vol surface, then the static one should also do. Otherwise, it is not possible for either of them...Am I right, am I wrong...??? I hope to be wrong in fact... Thanks for your help.

If it helps the following paper by Osajima gives an alternative expansion for the dynamic SABR. Here is more clear how the time dependent parameters input the model (see Theorem 1.1 equations (1.2)-(1.5))http://kyokan.ms.u-tokyo.ac.jp/users/pr ... 006-29.pdf

Hi.I knew the document but thanks for answering. I actually made my way through the model. There is no contradiction at all. I didn't get that you obtain different eta bar, v bar, theta bar for each maturity level and that each of them is consistent with the original time-dependent parameters. Calibration by bootstrapping is then easy to perform.Nevertheless, I faced another problem when the gamma(t) parameter is different from 1. The following degenerated case illustrates it:- constant params rho(t) = rho, gamma(t) = gamma <> 1- nu(t) = 0- beta = 1The model is thus reduced to a black process of constant volatility (gamma*alpha). Though, if I insert the parameters' values into the implied vol formula, all dependence in gamma disappears and everything reduces to (alpha).So, according to me, the formula doesn't hold when gamma <> 1. This is confirmed in simulation. So I finally forced gamma(t) = 1 and worked with a more simple (and less precise) model.

Hi gledI just read through this forum as I am working on a calibration of the dynamic SABR model at the moment. As you wrote that you have made it through the model, I have some questions and would be very happy if you could help me with them....Do you have any suggestions for the funvtion C(f) (maybe from articles abt it....) or are you using f^beta as in the static model?How do you bootstrap and calibrate eta bar, v bar and teta bar for the entire surface after extimating it for several maturities?Should not teta bar go to zero as v goes to v bar?ThanksThomas

If gled replies after more than 2 years and only 2 posts -- well, have you heard the story of Lazarus?