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Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform

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  • Michele Leonardo Bianchi
  • Gian Luca Tassinari

Abstract

In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models considered are a multivariate extension of the normal tempered stable (NTS) model and the generalized hyperbolic (GH) model, respectively, and the connection between the historical measure P and the risk-neutral measure Q is given by the Esscher transform. We consider an estimation method that simultaneously calibrate the time series of univariate log-returns and the univariate observed volatility smile. To calibrate the models, there is no need of liquid multivariate derivative quotes. The method is applied to fit a 50-dimensional series of stock returns, to evaluate widely known portfolio risk measures and to perform a portfolio selection analysis.

Suggested Citation

  • Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1805.05584
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    References listed on IDEAS

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    1. Sebastian Kring & Svetlozar T. Rachev & Markus Höchstötter & Frank J. Fabozzi & Michele Leonardo Bianchi, 2009. "Multi-tail generalized elliptical distributions for asset returns," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 272-291, July.
    2. DeMiguel, Victor & Plyakha, Yuliya & Uppal, Raman & Vilkov, Grigory, 2013. "Improving Portfolio Selection Using Option-Implied Volatility and Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(6), pages 1813-1845, December.
    3. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    4. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    5. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    6. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    7. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    8. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    9. Georg Mainik & Georgi Mitov & Ludger Ruschendorf, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Papers 1505.04045, arXiv.org.
    10. Taboga, Marco, 2016. "Option-implied probability distributions: How reliable? How jagged?," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 453-469.
    11. Ballotta, Laura & Deelstra, Griselda & Rayée, Grégory, 2017. "Multivariate FX models with jumps: Triangles, Quantos and implied correlation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1181-1199.
    12. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    13. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    14. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2018. "Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 339-378, March.
    15. Sara Cecchetti & Laura Sigalotti, 2013. "Forward-looking robust portfolio selection," Temi di discussione (Economic working papers) 913, Bank of Italy, Economic Research and International Relations Area.
    16. Gian Luca Tassinari & Michele Leonardo Bianchi, 2014. "Calibrating The Smile With Multivariate Time-Changed Brownian Motion And The Esscher Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
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    Cited by:

    1. Erindi Allaj, 2020. "The Black–Litterman model and views from a reverse optimization procedure: an out-of-sample performance evaluation," Computational Management Science, Springer, vol. 17(3), pages 465-492, October.
    2. Michele Leonardo Bianchi, 2018. "Are multi-factor Gaussian term structure models still useful? An empirical analysis on Italian BTPs," Papers 1805.09996, arXiv.org.
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    4. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Gamma Related Ornstein-Uhlenbeck Processes and their Simulation," Papers 2003.08810, arXiv.org.

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