A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing

2024/08/04 by Mark Stedman, Stedman, Mark, Luca Capriotti +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Physical sciences #Mathematical Finance (q-fin.MF) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2408.02064

openalex publication_date 2024/08/04 · openalex created_date 2024/10/14 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Using path integrals to price interest rate derivatives
• A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results
• A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods
• Path Integral Method for Pricing Proportional Step Double-Barrier Option with Time Dependent Parameters
• Path Dependent Option Pricing: the path integral partial averaging\n method