Efficient Simulation for Risk Measurement in Portfolio of CDOs

We consider a portfolio containing CDO tranches as well as ordinary bonds. Our interest is in large loss probabilities and risk measures such as value-at-risk. When loss is measured on amark-to-market basis, estimation via simulation requires a nested procedure: In the outer step one draws realizations of all risk factors up to the horizon, and in the inner step one re-prices each instrument in the portfolio at the horizon conditional on the drawn risk factors. Practitioners perceive the computational burden of such nested schemes to be unacceptable, and adopt a variety of somewhat ad hoc measures to avoid the inner simulation. In this paper, we question whether such short cuts are necessary. We show that a relatively small number of trials in the inner step can yield accurate estimates, and analyze how a fixed computational budget may be allocated to the inner and the outer step to minimize the mean square error of the resultant estimator.