Simulation of conditional expectations under fast mean-reverting stochastic volatility models
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.
Cite
@article{arxiv.2012.09726,
title = {Simulation of conditional expectations under fast mean-reverting stochastic volatility models},
author = {Andrei Cozma and Christoph Reisinger},
journal= {arXiv preprint arXiv:2012.09726},
year = {2021}
}