  In this short paper, we study the simulation of a large system of stochastic
processes subject to a common driving noise and fast mean-reverting stochastic
volatilities. This model may be used to describe the firm values of a large
pool of financial entities. We then seek an efficient estimator for the
probability of a default, indicated by a firm value below a certain threshold,
conditional on common factors. We consider approximations where coefficients
containing the fast volatility are replaced by certain ergodic averages (a type
of law of large numbers), and study a correction term (of central limit
theorem-type). The accuracy of these approximations is assessed by numerical
simulation of pathwise losses and the estimation of payoff functions as they
appear in basket credit derivatives.
