A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing
A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing ArXiv ID: 2408.02064 “View on arXiv” Authors: Unknown 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. ...