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The SEV-SV Model—Applications in Portfolio Optimization

Author

Listed:
  • Marcos Escobar-Anel

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
    These authors contributed equally to this work.)

  • Weili Fan

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
    These authors contributed equally to this work.)

Abstract

This paper introduces and studies a new family of diffusion models for stock prices with applications in portfolio optimization. The diffusion model combines (stochastic) elasticity of volatility (EV) and stochastic volatility (SV) to create the SEV-SV model. In particular, we focus on the SEV component, which is driven by an Ornstein–Uhlenbeck process via two separate functional choices, while the SV component features the state-of-the-art 4/2 model. We study an investment problem within expected utility theory (EUT) for incomplete markets, producing closed-form representations for the optimal strategy, value function, and optimal wealth process for two different cases of prices of risk on the stock. We find that when EV reverts to a GBM model, the volatility and speed of reversion of the EV have a strong impact on optimal allocations, and more aggressive (bull markets) or cautious (bear markets) strategies are hence recommended. For a model when EV reverts away from GBM, only the mean reverting level of the EV plays a role. Moreover, the presence of SV leads mainly to more conservative investment decisions for short horizons. Overall, the SEV plays a more significant role than SV in the optimal allocation.

Suggested Citation

  • Marcos Escobar-Anel & Weili Fan, 2023. "The SEV-SV Model—Applications in Portfolio Optimization," Risks, MDPI, vol. 11(2), pages 1-34, January.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:2:p:30-:d:1049784
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    References listed on IDEAS

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    1. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    2. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    3. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    4. Sun-Yong Choi & Jean-Pierre Fouque & Jeong-Hoon Kim, 2013. "Option pricing under hybrid stochastic and local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1157-1165, July.
    5. 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.
    6. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    7. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    8. MacBeth, James D & Merville, Larry J, 1980. "Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
    9. Gao, Jianwei, 2010. "An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 511-530, June.
    10. Kim, Jeong-Hoon & Yoon, Ji-Hun & Lee, Jungwoo & Choi, Sun-Yong, 2015. "On the stochastic elasticity of variance diffusions," Economic Modelling, Elsevier, vol. 51(C), pages 263-268.
    11. Yuen, K.C. & Yang, H. & Chu, K.L., 2001. "Estimation in the Constant Elasticity of Variance Model," British Actuarial Journal, Cambridge University Press, vol. 7(2), pages 275-292, June.
    12. Martino Grasselli, 2017. "The 4/2 Stochastic Volatility Model: A Unified Approach For The Heston And The 3/2 Model," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1013-1034, October.
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