Switching latent factor value-at-risk models for conditionally heteroskedastic portfolios: A comparative approach

Abstract

In this paper, a computationally efficient Monte Carlo-based latent factor modeling approach for portfolio Value-at-Risk (VaR) estimation is introduced. We examine whether the inclusion of conditional heteroskedasticity in financial returns, and taking into account for possible hidden (Markovian) “regime changes” in the latent correlation structure of the portfolio can enhance the accuracy of VaR forecasts. Practical details of training such models with the expectation-maximization algorithm are also discussed. In conjunction with an approximated version of the Kalman filter, we show how to calculate maximum likelihood estimates of the model parameters, and to yield inferences about the unobservable path of the common factors, their volatilities and the hidden state sequence of the Markov process. The methodology is illustrated by an example using data from the Tunisian foreign exchange market, over the period of the Tunisian revolution from January 02, 2010 to December 30, 2012. We found that this new specification exhibits a good fit to the data, improves the accuracy of VaR predictions of the Tunisian foreign public debt portfolio and reduces the number and average size of back-testing breaches when a financial crisis occurs.

Keywords:

• Latent factor models
• conditional heteroskedasticity
• hidden Markov models
• Kalman filter
• EM algorithm
• Monte Carlo VaR

Acknowledgments

We would like to thank the editor and two anonymous referees for their detailed and useful comments that greatly improved this paper.

Notes

1 https://www.bct.gov.tn/.