Path integral approach for time-dependent Hamiltonians with applications to derivative pricing.
basic_science · Level V
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- Record sourced from PubMed, PMID 39916258.
- Also identified by DOI 10.1103/PhysRevE.110.064113.
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Abstract
We generalize a semiclassical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)0031-900710.1103/PhysRevLett.55.912] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)0556-279110.1103/PhysRevA.34.5080] 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 make it a viable alternative to fully numerical schemes for a variety of applications in derivatives pricing.