I have the following problem regarding Equity-IR hybrid correlation and I would greatly appreciate any input/insight Instrument to price: a long-term equity option with stochastic IR. Model : We have Heston for EQ and a one-factor normal model for IR (G1 as in Brigo-Mercurio; to be specific). So, we have an Eq-IR and a Vol-IR correlation.Calibration : IR is calibrated to cap/floor and swaption vols using Lev-Mar. If there were no Eq-IR correl or vol-IR correls, we could have calibrated Heston to the option vol surface as usual. However, there are Eq-IR and vol-IR correls and not including these correls in the Equity option vol surface calibration would most certainly lead to mis-pricing in the pricing model. In other words, we would not be able to recover the market prices with this model b/c the correls are not part of the calibration (taken from historical data). Question : How does one go about including the aforementioned correls in the calibration? I have done some research but could not tell if there is a market standard technique to do this. Again, any response would be greatly appreciated.

hi,I guess G1 is just Hull/White?I'm not sure whether I really understood where your problem is.If you have an efficient vanilla pricer for the hybrid process you could eithertry to calibrate all remaining parameters or plug in some parameters (e.g. rates/equityvol) and calibrate the rest. As you will probably not try to hedge ir/equity correlation (do you?), I would go fora conservative assumption rather than trying to calibrate.regards, f.

Florian, the G1 parameters are no problem. Of the remaining params, one can calibrate only a subset of the parameters to Heston's option formula.So, two parameters namely Eq-IR correlation and Vol-IR correlation remain uncalibrated to market data. That's the problem.

hi, maybe I'm missing your point, but I'll try again.If you're calibrating "Heston as usual", then I suppose you're using Heston with deterministic rates.If you want to calibrate "Heston HW", then you're using a different model.Plain Vanillas can be solved via FDM or I guess some approximation, as here: http://ssrn.com/abstract=1382902(I haven't tried this approximation, but it looks interesting.)If you use this pricer than you could try to calibrate all the remaining parameters, but I guess theproblem will be ill-posed.So I would try to plug in fixed correlation assumptions and calibrate the rest.(resp. see how robust the other parameters are w.r.t. correlation assumptions.)I would be interested if other people do this differently. (I.e. try to imply/hedge equity/ir correlation.)regards, f.