Calibrating joint realized and implied-realized spreads

tradingquest · April 3rd, 2007, 3:58 pm

I am trying to calibrate a pair of stochastic equations to market data and am in need of some MLE /alternative literature references to accomplish that. I d really appreciate some inputs on the issue: To elaborate: The 2 equations are:1. Dsigma_realized(t) = alpha*(sigma_longtermaverage - sigma_realized)dt + w1 *dz1(t)2. D(sigma_implied - sigma_realized) = beta*(spread_longtermaverage - (sigma_implied - sigma_realized)) + w2* dz2(t)corr(dz1,dz2) = rho*dtPlease suggest ideas..Thanks