Optimal investment of variance-swaps in jump-diffusion market with regime-switching |
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| Institution: | 1. School of Mathematics and Statistics, Xidian University, Xian 710071, China;2. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;3. University of International Business and Economics, Beijing 100029, China;4. Business School, Nankai University, Tianjin 300071, China;1. School of Finance, Guangdong University of Finance and Economics, Guangzhou 510320, China;2. School of Banking and Finance, University of International Business and Economics, Beijing 100029, China;3. UQ Business School, The University of Queensland, St Lucia, QLD 4072, Australia;4. School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China |
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| Abstract: | We consider a general jump-diffusion market with regime-switching where the jump risk is modeled as a Markov-modulated Poisson random measure. In this incomplete market, we price the variance-swaps using a combination of the Esscher transform and change of measure on time-inhomogeneous Markov chains. We study the dynamic optimal investment problem of the variance-swaps and characterize the optimal feedback strategy. Moreover, a closed-form solution to the HJB PDE associated with the stochastic control problem is established and the verification theorem is proved. The numerical analysis based on a two-state Markov chain uncovers some robust features of the optimal investment strategy. |
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