Path integral approach for time-dependent Hamiltonians with applications to derivative pricing.

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.