Optimal investment in equity and VIX derivatives |
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| Authors: | Xiangzhen Yan Yunfan Zhu Zhenyu Cui Shuguang Zhang |
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| Affiliation: | 1.Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China2.School of Business, Stevens Institute of Technology, Hoboken, NJ 07030, USA |
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| 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 derivatives. Based on the closed-form formulas, we explicitly determine the portfolio improvements brought by the inclusion of the VIX derivatives and establish that it is theoretically positive. This justifies the economic intuition and observed demand for VIX derivatives in a portfolio management setting. Numerical examples illustrate the results. |
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| Keywords: | optimal investment stochastic control VIX derivatives HJB equation incomplete market |
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