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arXiv · 2012.09726

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

Andrei Cozma·Christoph Reisinger
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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.

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Andrei Cozma, Christoph Reisinger. 2020-12-17. Simulation of conditional expectations under fast mean-reverting stochastic volatility models. https://arxiv.org/abs/2012.09726

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