Pricing and Hedging of Discrete Dynamic Guaranteed Funds |
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| Authors: | Wai-Man Tse, Eric C. Chang&dagger , Leong Kwan Li&Dagger , Henry M. K. Mok§ |
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| Affiliation: | Wai-Man Tse is at Faculty of Business and Economics, The University of Hong Kong, Pokfulam Road, Hong Kong, and at Department of Finance, Chu Hai College of Higher Education, Tsuen, Wan, N. T., Hong Kong;. Eric C. Chang is at Faculty of Business and Economics, The University of Hong Kong, Pokfulam Road, Hong Kong;. Leong Kwan Li works with Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong;. Henry M. K. Mok is at Department of Decision Sciences and Managerial Economics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. |
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| Abstract: | We derive a risk‐neutral pricing model for discrete dynamic guaranteed funds with geometric Gaussian underlying security price process. We propose a dynamic hedging strategy by adding a gamma factor to the conventional delta. Simulation results demonstrate that, when hedging discretely, the risk‐neutral gamma‐adjusted‐delta strategy outperforms the dynamic delta hedging strategy by reducing the expected hedging error, lowering the hedging error variability, and improving the self‐financing possibility. The discrete dynamic delta‐only hedging not only causes potential overcharge to clients but also could be costly to the issuers. We show that a naive application of continuous‐time hedging formula to a discrete‐time hedging setting tends to worsen these possibilities. |
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