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Optimal market completion through financial derivatives with applications to volatility risk

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  • Matt Davison
  • Marcos Escobar-Anel
  • Yichen Zhu

Abstract

This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We introduce an efficient and accurate simulation-based method, applicable to generalized diffusion models, to approximate the optimal derivatives-based portfolio strategy. We build upon the double optimization approach (i.e. expected utility maximization and risk exposure minimization) proposed in Escobar-Anel et al. (2022); demonstrating that strangle options are the best choices for market completion within equity options. Furthermore, we explore the benefit of using volatility index derivatives and conclude that they could be more convenient substitutes when only long-term maturity equity options are available.

Suggested Citation

  • Matt Davison & Marcos Escobar-Anel & Yichen Zhu, 2022. "Optimal market completion through financial derivatives with applications to volatility risk," Papers 2202.08148, arXiv.org.
    • Handle: RePEc:arx:papers:2202.08148
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    1. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
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    10. 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.
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    12. Zhu, Yichen & Escobar-Anel, Marcos, 2022. "Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models," Applied Mathematics and Computation, Elsevier, vol. 418(C).
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