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Optimal Option Portfolios for Student t Returns

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  • Kyle Sung
  • Traian A. Pirvu

Abstract

We provide an explicit solution for optimal option portfolios under variance and Value at Risk (VaR) minimization when the underlying returns follow a Student t-distribution. The novelty of our paper is the departure from the traditional normal returns setting. Our main contribution is the methodology for obtaining optimal portfolios. Numerical experiments reveal that, as expected, the optimal variance and VaR portfolio compositions differ by a significant amount, suggesting that more realistic tail risk settings can lead to potentially more realistic portfolio allocations.

Suggested Citation

  • Kyle Sung & Traian A. Pirvu, 2026. "Optimal Option Portfolios for Student t Returns," Papers 2601.07991, arXiv.org.
    • Handle: RePEc:arx:papers:2601.07991
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    References listed on IDEAS

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    1. Michael R. Metel & Traian A. Pirvu & Julian Wong, 2015. "Risk management under Omega measure," Papers 1510.05790, arXiv.org, revised Apr 2017.
    2. Liurui Deng & Traian A. Pirvu, 2019. "Multi-Period Investment Strategies under Cumulative Prospect Theory," JRFM, MDPI, vol. 12(2), pages 1-15, May.
    3. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2016. "Risk minimization and portfolio diversification," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1325-1332, September.
    4. Siven, Johannes Vitalis & Lins, Jeffrey Todd & Szymkowiak-Have, Anna, 2009. "Value-at-Risk computation by Fourier inversion with explicit error bounds," Finance Research Letters, Elsevier, vol. 6(2), pages 95-105, June.
    5. Wenbo Hu & Alec Kercheval, 2010. "Portfolio optimization for student t and skewed t returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 91-105.
    6. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    7. Aditya Maheshwari & Traian A. Pirvu, 2020. "Portfolio Optimization under Correlation Constraint," Risks, MDPI, vol. 8(1), pages 1-18, February.
    8. Chen, Rongda & Yu, Lean, 2013. "A novel nonlinear value-at-risk method for modeling risk of option portfolio with multivariate mixture of normal distributions," Economic Modelling, Elsevier, vol. 35(C), pages 796-804.
    9. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
    10. Francesco Cesarone & Manuel L. Martino & Fabio Tardella, 2023. "Mean-Variance-VaR portfolios: MIQP formulation and performance analysis," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 1043-1069, September.
    11. Pang, Xiaochuan & Zhu, Shushang & Cui, Xueting & Ma, Jiali, 2023. "Systemic risk of optioned portfolio: Controllability and optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    12. Michael R. Metel & Traian A. Pirvu & Julian Wong, 2017. "Risk Management under Omega Measure," Risks, MDPI, vol. 5(2), pages 1-14, May.
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    14. Liurui Deng & Traian A. Pirvu, 2016. "Multi-period investment strategies under Cumulative Prospect Theory," Papers 1608.08490, arXiv.org, revised Mar 2019.
    15. Zhu, Shushang & Zhu, Wei & Pei, Xi & Cui, Xueting, 2020. "Hedging crash risk in optimal portfolio selection," Journal of Banking & Finance, Elsevier, vol. 119(C).
    16. Ahmad Reza Yazdanian & T A Pirvu, 2014. "Numerical analysis for Spread option pricing model in illiquid underlying asset market: full feedback model," Papers 1406.1149, arXiv.org.
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