Mean‐variance hedging with basis risk
Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuitie...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/149141 |
| _version_ | 1824456038487687168 |
|---|---|
| author | Xue, Xiaole Zhang, Jingong Weng, Chengguo |
| author2 | Nanyang Business School |
| author_facet | Nanyang Business School Xue, Xiaole Zhang, Jingong Weng, Chengguo |
| author_sort | Xue, Xiaole |
| collection | NTU |
| description | Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuities, etc. In the presence of basis risk, a perfect hedging is impossible, and in this paper, we adopt a mean‐variance criterion to strike a balance between the expected hedging error and its variability. Under a time‐dependent diffusion model setup, explicit optimal solutions are derived for the hedging target being either a European option or a forward contract. The solutions are obtained by a delicate application of the linear quadratic control theory, the method of backward stochastic differential equation, and Malliavin calculus. A numerical example is presented to illustrate our theoretical results and their interesting implications. |
| first_indexed | 2025-02-19T03:47:45Z |
| format | Journal Article |
| id | ntu-10356/149141 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:47:45Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1491412023-05-19T07:31:18Z Mean‐variance hedging with basis risk Xue, Xiaole Zhang, Jingong Weng, Chengguo Nanyang Business School Business::Finance Optimal Hedging Basis Risk Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuities, etc. In the presence of basis risk, a perfect hedging is impossible, and in this paper, we adopt a mean‐variance criterion to strike a balance between the expected hedging error and its variability. Under a time‐dependent diffusion model setup, explicit optimal solutions are derived for the hedging target being either a European option or a forward contract. The solutions are obtained by a delicate application of the linear quadratic control theory, the method of backward stochastic differential equation, and Malliavin calculus. A numerical example is presented to illustrate our theoretical results and their interesting implications. Accepted version Xue acknowledges financial support from the China Scholarship Council (No.: 201606220132) and the research facilities offered by University of Waterloo during his visit. Zhang thanks financial support from the Society of Actuaries (SOA) Hickman Scholarship and the Department of Statistics and Actuarial Science, University of Waterloo. Weng acknowledges the financial support from the Natural Sciences and Engineering Research Council of Canada (RGPIN-2016- 04001), SOA Centers of Actuarial Excellence Research Grant, and the National Natural Science Foundation of China (No. 71671104). 2021-05-19T03:10:05Z 2021-05-19T03:10:05Z 2019 Journal Article Xue, X., Zhang, J. & Weng, C. (2019). Mean‐variance hedging with basis risk. Applied Stochastic Models in Business and Industry, 35(3), 704-716. https://dx.doi.org/10.1002/asmb.2380 1526-4025 https://hdl.handle.net/10356/149141 10.1002/asmb.2380 3 35 704 716 en Applied Stochastic Models in Business and Industry This is the peer reviewed version of the following article: Xue, X., Zhang, J. & Weng, C. (2019). Mean‐variance hedging with basis risk. Applied Stochastic Models in Business and Industry, 35(3), 704-716. https://dx.doi.org/10.1002/asmb.2380, which has been published in final form at https://doi.org/10.1002/asmb.2380. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. application/pdf |
| spellingShingle | Business::Finance Optimal Hedging Basis Risk Xue, Xiaole Zhang, Jingong Weng, Chengguo Mean‐variance hedging with basis risk |
| title | Mean‐variance hedging with basis risk |
| title_full | Mean‐variance hedging with basis risk |
| title_fullStr | Mean‐variance hedging with basis risk |
| title_full_unstemmed | Mean‐variance hedging with basis risk |
| title_short | Mean‐variance hedging with basis risk |
| title_sort | mean variance hedging with basis risk |
| topic | Business::Finance Optimal Hedging Basis Risk |
| url | https://hdl.handle.net/10356/149141 |
| work_keys_str_mv | AT xuexiaole meanvariancehedgingwithbasisrisk AT zhangjingong meanvariancehedgingwithbasisrisk AT wengchengguo meanvariancehedgingwithbasisrisk |