Optimal investment in equity and VIX derivatives

Xiangzhen Yan, Yunfan Zhu, Zhenyu Cui, Shuguang Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

We solve in closed-form the optimal investment strategies in equity and VIX derivatives in a stochastic volatility model with jumps. Our framework includes both complete market and incomplete market cases, when diffusive risk, volatility risk and jump risk are present. VIX derivatives allow for direct exposure to volatility risk compared to equity de-rivatives. Based on the closed-form formula, we explicitly determine the portfolio improvement brought by the inclusion of the VIX derivative and establish that it is theoretically positive. This justifies the economic intuition and observed de-mand for VIX derivatives in a portfolio management setting. Numerical examples illustrate the results.

Original languageEnglish
Article number6
JournalJournal of University of Science and Technology of China
Volume53
Issue number2
DOIs
StatePublished - 28 Feb 2023

Keywords

  • HJB equation
  • VIX derivatives
  • incomplete market
  • optimal investment
  • stochastic control

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