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A time consistent derivative strategy

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  • Walter Mudzimbabwe

    (Department of Mathematics, University of Zimbabwe, P. O. Box MP 167, Mount Pleasant, Harare, Zimbabwe2School of Computer Science and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braamfontein 2000, Johannesburg, South Africa)

Abstract

In this paper, we derive a time consistent investment strategy for an investor who can invest not only in a bond and stock but in a derivative as well. In order to capture typical features shown by stocks, the stock and by extension the derivative depends on stochastic volatility. We assume that the investor is interested in maximizing a mean–variance utility function. Since the problem is time-inconsistent, we formulate the problem in game theoretic way and seek a subgame Nash equilibrium as the strategy. By solving an extended HJB equation system, we derive explicit time-consistent strategy and the corresponding efficient frontier. In order to show efficiency of the derivative strategy, we compare it with a strategy for the case of a market without a derivative. Our results show that efficient frontier for an investor with a derivative is higher than without derivative.

Suggested Citation

  • Walter Mudzimbabwe, 2020. "A time consistent derivative strategy," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-25, March.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:01:n:s2424786320500048
    DOI: 10.1142/S2424786320500048
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    References listed on IDEAS

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    1. Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    2. Shen, Yang & Zeng, Yan, 2015. "Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 118-137.
    3. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    4. Wu, Huiling & Zhang, Ling & Chen, Hua, 2015. "Nash equilibrium strategies for a defined contribution pension management," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 202-214.
    5. Li, Danping & Rong, Ximin & Zhao, Hui, 2015. "Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 28-44.
    6. Li, Zhongfei & Zeng, Yan & Lai, Yongzeng, 2012. "Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 191-203.
    7. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    8. Yuan-Hung Hsuku, 2007. "Dynamic consumption and asset allocation with derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 137-149.
    9. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2015. "Robust portfolio choice with derivative trading under stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 142-157.
    10. K. Ronnie Sircar & George Papanicolaou, 1999. "Stochastic volatility, smile & asymptotics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 107-145.
    11. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
    12. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    13. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    14. Aytaç Ílhan & Mattias Jonsson & Ronnie Sircar, 2005. "Optimal investment with derivative securities," Finance and Stochastics, Springer, vol. 9(4), pages 585-595, October.
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