Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach
No-arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist in various fields, even for a very short time. By knowing that an arbitrage property exists, we can adopt a financial trading strategy. This paper investigates the inverse option...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-02-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037422000760 |
| _version_ | 1797895585206894592 |
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| author | Yasushi Ota Yu Jiang Daiki Maki |
| author_facet | Yasushi Ota Yu Jiang Daiki Maki |
| author_sort | Yasushi Ota |
| collection | DOAJ |
| description | No-arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist in various fields, even for a very short time. By knowing that an arbitrage property exists, we can adopt a financial trading strategy. This paper investigates the inverse option problems (IOP) in the backward parabolic equation with a suitable initial condition in financial markets. We identify the coefficients of this problem from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the artificial measured data and the real financial market data. |
| first_indexed | 2024-04-10T07:28:13Z |
| format | Article |
| id | doaj.art-f6cdcfaa2c5b441bb2458fc6cca63e56 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-10T07:28:13Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-f6cdcfaa2c5b441bb2458fc6cca63e562023-02-24T04:31:33ZengElsevierResults in Applied Mathematics2590-03742023-02-0117100353Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approachYasushi Ota0Yu Jiang1Daiki Maki2Faculty of Business Administration St. Andrew’s University, 1-1, Manabino, Izumi City, Osaka, Japan; Corresponding author.School of Mathematics Shanghai University of Finance and Economics, 777 Guoding Rd. Shanghai, 200433, PR ChinaFaculty of Commerce Doshisha University, Karasuma-higashi-iru, Imadegawa-dori, Kamigyo-ku, Kyoto, JapanNo-arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist in various fields, even for a very short time. By knowing that an arbitrage property exists, we can adopt a financial trading strategy. This paper investigates the inverse option problems (IOP) in the backward parabolic equation with a suitable initial condition in financial markets. We identify the coefficients of this problem from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the artificial measured data and the real financial market data.http://www.sciencedirect.com/science/article/pii/S2590037422000760Option pricingInverse problemBayesian inference approach |
| spellingShingle | Yasushi Ota Yu Jiang Daiki Maki Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach Results in Applied Mathematics Option pricing Inverse problem Bayesian inference approach |
| title | Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach |
| title_full | Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach |
| title_fullStr | Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach |
| title_full_unstemmed | Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach |
| title_short | Parameters identification for an inverse problem arising from a binary option using a Bayesian inference approach |
| title_sort | parameters identification for an inverse problem arising from a binary option using a bayesian inference approach |
| topic | Option pricing Inverse problem Bayesian inference approach |
| url | http://www.sciencedirect.com/science/article/pii/S2590037422000760 |
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