Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929337297534976 |
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| author | Kędra, Jarek Libman, Assaf Steblovskaya, Victoria |
| author_facet | Kędra, Jarek Libman, Assaf Steblovskaya, Victoria |
| contents | We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide explicit formulas for the minimum cost super-hedging strategies for a wide class of European type multi-asset contingent claims. This class includes European basket call and put options, among others. Since a super-hedge is a non-self-financing arbitrage strategy, it produces non-negative local residuals, for which we also give explicit formulas. This paper completes the foundation started in previous work of the authors for the extension of our results to a more realistic market model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02912 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market Kędra, Jarek Libman, Assaf Steblovskaya, Victoria Mathematical Finance We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide explicit formulas for the minimum cost super-hedging strategies for a wide class of European type multi-asset contingent claims. This class includes European basket call and put options, among others. Since a super-hedge is a non-self-financing arbitrage strategy, it produces non-negative local residuals, for which we also give explicit formulas. This paper completes the foundation started in previous work of the authors for the extension of our results to a more realistic market model. |
| title | Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2301.02912 |