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

Area of Science:

• Quantitative Finance
• Computational Physics

Background:

• Semiclassical path integral methods are established in physics.
• Existing methods struggle with time-dependent Hamiltonians in finance.

Purpose of the Study:

• Generalize semiclassical path integral approach for time-dependent Hamiltonians.
• Apply the method to financial derivative pricing.
• Evaluate accuracy and efficiency for intractable models.

Main Methods:

• Generalization of Giachetti-Tognetti and Feynman-Kleinert semiclassical path integral methods.
• Application to time-dependent Hamiltonians.
• Testing on the Black-Karasinski interest rate model.

Main Results:

• The generalized path integral approach accurately prices financial derivatives.
• Demonstrated effectiveness on the analytically intractable Black-Karasinski model.
• The method shows computational efficiency.

Conclusions:

• The generalized semiclassical path integral method is a viable alternative for derivatives pricing.
• Extends applicability to complex, time-dependent financial models.
• Offers accuracy and computational efficiency over traditional numerical schemes.