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

Author

Listed:
  • Marcos Escobar-Anel

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A5B7, Canada
    These authors contributed equally to this work.)

  • Zhenxian Gong

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A5B7, Canada
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Marcos Escobar-Anel & Zhenxian Gong, 2021. "Mean-Reverting 4/2 Principal Components Model. Financial Applications," Risks, MDPI, vol. 9(8), pages 1-23, July.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:8:p:141-:d:602549
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    References listed on IDEAS

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    4. Langetieg, Terence C, 1980. "A Multivariate Model of the Term Structure," Journal of Finance, American Finance Association, vol. 35(1), pages 71-97, March.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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