Mean-Reverting 4/2 Principal Components Model. Financial Applications

Marcos Escobar-Anel and Zhenxian Gong
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Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A5B7, Canada
Zhenxian Gong: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A5B7, Canada
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Risks, 2021, vol. 9, issue 8, 1-23

Abstract: In this paper, we propose a new multivariate mean-reverting model incorporating state-of-the art 4/2 stochastic volatility and a convenient principal component stochastic volatility (PCSV) decomposition for the stochastic covariance. We find a quasi closed-form characteristic function and propose analytic approximations, which aid in the pricing of derivatives and calculation of risk measures. Parameters are estimated on three bivariate series, using a two-stage methodology involving method of moments and least squares. Moreover, a scaling factor is added for extra degrees of freedom to match data features. As an application, we consider investment strategies for a portfolio with two risky assets and a risk-free cash account. We calculate value-at-risk (VaR) values at a 95% risk level using both simulation-based and distribution-based methods. A comparison of these VaR values supports the effectiveness of our approximations and the potential for higher dimensions.

Keywords: principal component analysis; 4/2 stochastic volatility model; moment-generating function; risk management calculations (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:9:y:2021:i:8:p:141-:d:602549

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