  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.
