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Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model

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  • M. Escobar-Anel
  • M. Kschonnek
  • R. Zagst

Abstract

We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston's stochastic volatility model. We apply existing duality methods to obtain a closed-form expression for the optimal portfolio allocation. In doing so, we observe that allocation constraints impact the optimal constrained portfolio allocation in a fundamentally different way in Heston's stochastic volatility model than in the Black Scholes model. In particular, the optimal constrained portfolio may be different from the naive ‘capped’ portfolio, which caps off the optimal unconstrained portfolio at the boundaries of the constraints. Despite this difference, we illustrate by way of a numerical analysis that in most realistic scenarios the capped portfolio leads to slim annual wealth equivalent losses compared to the optimal constrained portfolio. During a financial crisis, however, a capped solution might lead to compelling annual wealth equivalent losses.

Suggested Citation

  • M. Escobar-Anel & M. Kschonnek & R. Zagst, 2023. "Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 23(12), pages 1793-1813, November.
    • Handle: RePEc:taf:quantf:v:23:y:2023:i:12:p:1793-1813
    DOI: 10.1080/14697688.2023.2271223
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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Thibaut Moyaert & Mikael Petitjean, 2011. "The performance of popular stochastic volatility option pricing models during the subprime crisis," Applied Financial Economics, Taylor & Francis Journals, vol. 21(14), pages 1059-1068.
    3. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    4. Yuyang Cheng & Marcos Escobar-Anel, 2021. "Optimal investment strategy in the family of 4/2 stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(10), pages 1723-1751, October.
    5. Carl Lindberg, 2006. "NEWS‐GENERATED DEPENDENCE AND OPTIMAL PORTFOLIOS FOR n STOCKS IN A MARKET OF BARNDORFF‐NIELSEN AND SHEPHARD TYPE," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 549-568, July.
    6. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    7. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    8. Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    9. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    10. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    11. Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    14. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2023. "Portfolio Optimization with Allocation Constraints and Stochastic Factor Market Dynamics," Papers 2303.09835, arXiv.org.
    15. Branger, Nicole & Schlag, Christian & Schneider, Eva, 2008. "Optimal portfolios when volatility can jump," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1087-1097, June.
    16. Egloff, Daniel & Leippold, Markus & Wu, Liuren, 2010. "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(5), pages 1279-1310, October.
    17. Jan Kallsen & Johannes Muhle-Karbe, 2010. "Utility Maximization In Affine Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 459-477.
    18. repec:dau:papers:123456789/1392 is not listed on IDEAS
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