Model-free bounds for multi-asset options using option-implied information and their exact computation
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices fo...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/169333 |
| _version_ | 1811677976349114368 |
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| author | Neufeld, Ariel Papapantoleon, Antonis Xiang,Qikun |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Neufeld, Ariel Papapantoleon, Antonis Xiang,Qikun |
| author_sort | Neufeld, Ariel |
| collection | NTU |
| description | We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives and even allow for the presence of bid–ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problem over vectors, subject to certain constraints. Then, we recast this problem into a linear semi-infinite optimization problem and provide two algorithms for its solution. These algorithms provide upper and lower bounds for the prices that are ε-optimal, as well as a characterization of the optimal pricing measures. These algorithms are efficient and allow the computation of bounds in high-dimensional scenarios (e.g., when d = 60). Moreover, these algorithms can be used to detect arbitrage opportunities and identify the corresponding arbitrage strategies. Numerical experiments using both synthetic and real market data showcase the efficiency of these algorithms, and they also allow understanding of the reduction of model risk by including additional information in the form of known derivative prices. |
| first_indexed | 2024-10-01T02:45:55Z |
| format | Journal Article |
| id | ntu-10356/169333 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:45:55Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1693332023-07-17T15:34:51Z Model-free bounds for multi-asset options using option-implied information and their exact computation Neufeld, Ariel Papapantoleon, Antonis Xiang,Qikun School of Physical and Mathematical Sciences Science::Mathematics Model-Free Bounds Option-Implied Information We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic setting, in that we only assume the knowledge of traded prices for other single- and multi-asset derivatives and even allow for the presence of bid–ask spread in these prices. We provide a fundamental theorem of asset pricing for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problem over vectors, subject to certain constraints. Then, we recast this problem into a linear semi-infinite optimization problem and provide two algorithms for its solution. These algorithms provide upper and lower bounds for the prices that are ε-optimal, as well as a characterization of the optimal pricing measures. These algorithms are efficient and allow the computation of bounds in high-dimensional scenarios (e.g., when d = 60). Moreover, these algorithms can be used to detect arbitrage opportunities and identify the corresponding arbitrage strategies. Numerical experiments using both synthetic and real market data showcase the efficiency of these algorithms, and they also allow understanding of the reduction of model risk by including additional information in the form of known derivative prices. Nanyang Technological University Submitted/Accepted version This work was supported by the Nanyang Technological University [NAP Grant] and the Hellenic Foundation for Research and Innovation [Grant HFRI-FM17-2152]. 2023-07-13T02:48:04Z 2023-07-13T02:48:04Z 2023 Journal Article Neufeld, A., Papapantoleon, A. & Xiang, Q. (2023). Model-free bounds for multi-asset options using option-implied information and their exact computation. Management Science, 69(4), 2051-2068. https://dx.doi.org/10.1287/mnsc.2022.4456 0025-1909 https://hdl.handle.net/10356/169333 10.1287/mnsc.2022.4456 2-s2.0-85156091245 4 69 2051 2068 en NAP Management Science © 2022 INFORMS. All rights reserved. This paper was published in Management Science and is made available with permission of INFORMS. application/pdf |
| spellingShingle | Science::Mathematics Model-Free Bounds Option-Implied Information Neufeld, Ariel Papapantoleon, Antonis Xiang,Qikun Model-free bounds for multi-asset options using option-implied information and their exact computation |
| title | Model-free bounds for multi-asset options using option-implied information and their exact computation |
| title_full | Model-free bounds for multi-asset options using option-implied information and their exact computation |
| title_fullStr | Model-free bounds for multi-asset options using option-implied information and their exact computation |
| title_full_unstemmed | Model-free bounds for multi-asset options using option-implied information and their exact computation |
| title_short | Model-free bounds for multi-asset options using option-implied information and their exact computation |
| title_sort | model free bounds for multi asset options using option implied information and their exact computation |
| topic | Science::Mathematics Model-Free Bounds Option-Implied Information |
| url | https://hdl.handle.net/10356/169333 |
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