Popular SV models (e.g. Heston) all seem to assume a constant correlation between the underlier and vol/variance even though both underlier vol and vol vol move around dramatically. This seems odd on the face of it, and also considering that most people would expect equity-equity correlation to rise significantly during a market crash; why not equity-vol correlation too?A couple of years ago I was playing around with a model that allowed for a fairly arbitrary correlation skew, but I had to put it aside to work on something else. I’m thinking of dusting it off, and to the best of my knowledge there are still no popular SV models incorporating correlation skew for equity and fx.My first question is whether I’ve overlooked any models that address this.The second is whether anyone would be interested in taking a look at the paper I wrote on the model and commenting on whether it’s worth updating.There are some other aspects of the model that are fairly interesting.On short time scales (weeks) the model behaves somewhat like local volatility in that instantaneous vol is tied to the underlier level. But on longer time scales instantaneous vol depends on a dimensionless value so it depends only on something like moneyness.The behavior of correlation in the smile (fx) case is also quite unusual. It is not possible for instantaneous correlation to be zero in this model. Smiles occur because the correlation can flip sign and average to zero over time. This seems quite implausible but I did some analysis of historical fx data which showed significant support for flips in the sign of fx / fx vol correlation (included in the paper).If anyone is interested send me a message and I’ll email a copy of the paper.Ron

I am interested in reading this paper. It sounds really interesting to me. But I wonder how you will be able to calibrate it.

> But I wonder how you will be able to calibrate it. <The calibration is a very interesting problem. The calibrations in the paper are based on simultaneously fitting currently observed option prices plus historical variance swap prices. The latter carry a lot of information about volatility-of-volatility and volatility-underlier correlation. My experience is that the Heston model has trouble reproducing it, especially for fx (Heston implied volatility-of-volatility was far above historical volatility-of-volatility at the time I was writing the paper). Of course this can get into technical question about mixing different measures (the model includes a market price of volatility risk to help address this) and practical questions about how much history to use, but if the fitted parameters vary a lot over short terms the model probably isn't useful except as a price-interpolator for vanilla products anyway.Before you ask, the market price of volatility risk is determined as part of the calibration by basically asserting a spread between future realized and implied variance as another simultaneous part of the fit, with the spread value being determined from historical studies or your favorite crystal ball.I've been toying with the idea of including two or more days of option prices in the fit. This means fitting all the deltas as well as the prices, which gives some more information on the asset dynamics. The variance swap prices only capture particular subsets of this, but very efficiently so you can use as much history as you think appropriate.If you send me an email address I'll forward the paper.Ron

I'd be very interested in reading your paper. Please send it to tourkine@yahoo.com.

I would be very interested in reading your paper - please could you fwd it to s.krol@libertysurf.fr

I think I need to expand on the calibration issue and how the historical variance swap data is used.The framework is a two factor model where the second factor is unobservable and controls instantaneous volatility, correlation, and potentially all the other process parameters. Since the second factor is unobserved for each day included in the calibration (either as option data or variance-swap data) the vol-factor value must be included in the fit as a value to be determined in the fitting process. This effectively converts the time series of historical variance swap prices into a time series of fitted vol-factor values.Since the underlier factor is known we now can look at the changes in the two factors between successive observations, calculate the likelihood of this given the process parameters and include the likelihoods in the objective function being minimized. I also include the likelihood of the absolute level of the farthest-back in time of the vol factors.

I forgot to give you my email address: peter.leoni@mail.com

I would be interested in reading your paper. I also agree that there should be a correlation skew

please send it to avshie@hotmail.com

Hello thanks very much i am a student also writting a paper on vol_of_vol in FX. could you please send it to bayram.dincer@student.unisg.chthanks very much for the paper.