dear all I'm looking to calculate the vega of an exotic product using a monte carlo simulation and heston model.For the delta, it is quite simple (just need to shift the original spot and keep everything else identical, especially the random values), but for the vega I have no idea because it is a stochastic vol model...any answer?thank you!

price, then bump vol surface, recalibrate and reprice? either that, or for the 1% vega bump, you can shift the initial variance to account for a surface 1% higher (not guaranteed to fit the new surface but it's not million miles off)

The first method is very time consuming, and unfortunately the second one doesn't seem to workedit: if i shift the initial vol and the long term vol, the result gets a lot better, but the error is still important

maybe i'll be luckier after one week how can I shift the implied volatility surface using Heston Model ? The idea would be to shift the parameters of the model only...thank you

At first you should define what Vega in the Heston Model is. One possibility is to shift the input volatilities by 1% another is to use a different start variance, ...Maybe it is better to calculate the derivatites w.r.t. to paramaters of the used model (s0, v0, theta, kappa, sigma, rho, ...) and not w.r.t. parameters of other models like Black/Scholes?

let me clarifyi have calibrated the heston model (well, double-heston) using the implied vol surface of sx5e to price exotic products, this works finenow, i'd like to see the impact on the price of a shift of 1% of the whole implied vol surface, but the problem is that i don't have an implied vol surface anymore, i only have the parameters (initial variance, long term vol, vol of vol, correl etc)my goal is then very simple: i'm looking for a very simple method to find a new set of heston parameters which would give an additive shift of the implied vol surfaceex: i have a set of parameters X. i calculate the IV for many K/T, i get (normally) the same market vol surface. Now I need a set of parameters Y which will give me the same vol surface + 1% everywhere, without doing again the calibration processas said, bumping the init variance and/or the long term vol does not work properly

This is pretty standard. You first determine your Heston vega, i.e. the change in PV by bumping each single Heston param in turn and re-evaluating your trade. Through your calibration closed form formula you should also have a matrix relating the Heston params to the market implied vol surface. What you want is the inverse relationship, i.e. the shifts in Heston params needed to produce a given shift in the market implied vol surface. The answer is of course to perform a matrix inversion. Note that the inversion process is non-trivial as the matrix is typically ill-conditioned. The tricks to do the job and to fill the gaps to this brief answer of mine is, to quote a favourite ex-professor of mine, an exercise left to the reader.

i'm not sure to understand.. could you be more specific please?right now, what i'm doing is very simple: after the calibration, i calculate the IV for all exchange traded options that i used during the calibration, i shift them all by 1%, recalculate the option prices with BS, and re-calibrate (i use prices and not IV for the calibration process). It works fine but takes some time of course.