Calibrating Stoch. Intensity Process to Itraxx Index
Posted: August 27th, 2006, 4:05 pm
Hi,I am trying to calibrate a CDO model i have written to iTraxx data. I have a few years of index data and tranche prices. I am working within the reduced form framework where i model default intensity as a CIR + Jump, i.e. dlambda(t) = kappa*(theta-lambda(t) )*dt + sigma*sqrt(lambda(t) )*dW(t) + dJ(t) This leads to a closed form for survival(and thus default) probability, i.e. prob survival over[0,T] = exp (a(T) + b(T)*lambda(0) ) , for some a,b. I am assuming that my CDO pool is homogenous, such that I can use the iTraxx index to calibrate the above process. My question is therefore how do I calibrate this to my iTraxx data???!! A few further questions..1. survival prob is a function of lambda, this is stochastic, therefore when calibrating can i just set lambda to its long run mean??!! 2. in this model, the long-run mean of lambda is not dependent on sigma, therefore how to calibrate this?3. how to calibrate for my correlation parameter??"Any help is much appreciated!!Rgds,Ren.