A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909279673384960 |
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| author | Stedman, Mark Capriotti, Luca |
| author_facet | Stedman, Mark Capriotti, Luca |
| contents | We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach makes it a viable alternative to fully-numerical schemes for a variety of applications in derivatives pricing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing Stedman, Mark Capriotti, Luca Computational Finance Mathematical Finance Quantum Physics We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach makes it a viable alternative to fully-numerical schemes for a variety of applications in derivatives pricing. |
| title | A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing |
| topic | Computational Finance Mathematical Finance Quantum Physics |
| url | https://arxiv.org/abs/2408.02064 |