Hello,I am implementing the C.I.R. model of interest rate with Heston's stochasic volatility. So far I was able to find long-run mean mju and reverting "strength" kappa for both rate and volatility, but I still have no clue how to get the "volatility of volatility" parameter xi and correlation between volatility and rate stochastic terms rho.. Any suggestions?More precisely, the Model dr(t) = kappa1*(mju1-r(t))*dt + sqroot(r(t)*s(t))dW(t) - rate processds(t) = kappa2*(mju2-s(t))*dt+xi*sqroot(s(t))dV(t) - volatility processdr(t)ds(t) = rho*dtHow can I find the covariation matrix of the system from the historical data? With stochastic vol. the covariation changes over time..Thank you in advance!

QuoteOriginally posted by: GuestHello,I am implementing the C.I.R. model of interest rate with Heston's stochasic volatility. So far I was able to find long-run mean mju and reverting "strength" kappa for both rate and volatility, but I still have no clue how to get the "volatility of volatility" parameter xi and correlation between volatility and rate stochastic terms rho.. Any suggestions?More precisely, the Model dr(t) = kappa1*(mju1-r(t))*dt + sqroot(r(t)*s(t))dW(t) - rate processds(t) = kappa2*(mju2-s(t))*dt+xi*sqroot(s(t))dV(t) - volatility processdr(t)ds(t) = rho*dtHow can I find the covariation matrix of the system from the historical data? With stochastic vol. the covariation changes over time..Thank you in advance!1) Broadly, the parameters will "fall into your lap" when you fit the model to observable option prices. I suppose that's not what you mean.2) <<Covariation changes over time>> Then you should measure it with respect to a certain "tenor." That is, use the covariance from 1-month returns for a 1-month expiry, and so on...

ah... I just forgot to mention that there are no options on that rate as far as I know. So, I can calibrate using only the rate data (and the historical volatility data).

QuoteOriginally posted by: Guestah... I just forgot to mention that there are no options on that rate as far as I know. So, I can calibrate using only the rate data (and the historical volatility data).Well forget the "historical volatility data" because it probably doesn't go with your rates data. 1) Pick a "tenor," i.e. 1-Month, compile a histogram of returns for that.2) Use your model and try to solve for the parameters that give a histogram with the same distribution.I suppose you could use a K-S test (clumsy) to measure the goodness of your fit. Or model each histogram using kernel-density estimators (but that's just another belief system).Anyways, sorry but I think we're still speaking in generalities. Hope it helps.