Simulation of conditional expectations under fast mean-reverting stochastic volatility models

TL;DR

This paper develops efficient simulation methods for large systems of stochastic processes with fast mean-reverting stochastic volatility, focusing on estimating default probabilities conditioned on common factors, with applications to basket credit derivatives.

Contribution

It introduces approximation techniques replacing fast volatility coefficients with ergodic averages and analyzes correction terms, enhancing simulation efficiency for credit risk models.

Findings

Approximate default probabilities using ergodic averages.

Correction terms improve accuracy of simulations.

Numerical results validate the proposed methods.

Abstract

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.