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

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  • Andrei Cozma
  • Christoph Reisinger

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.

Suggested Citation

  • Andrei Cozma & Christoph Reisinger, 2020. "Simulation of conditional expectations under fast mean-reverting stochastic volatility models," Papers 2012.09726, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2012.09726
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    File URL: http://arxiv.org/pdf/2012.09726
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