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.
Keywords: Path integral approach, Black-Karasinski model, Derivatives pricing, Interest rates, Semi-classical approximation, Fixed Income (Interest Rates)
Complexity vs Empirical Score
- Math Complexity: 9.0/10
- Empirical Rigor: 6.0/10
- Quadrant: Holy Grail
- Why: The paper is mathematically dense, deriving a generalization of a semi-classical path integral method using advanced physics formalism for time-dependent Hamiltonians. Empirically, it demonstrates accuracy on the Black-Karasinski model and claims computational efficiency, but the excerpt lacks detailed implementation or backtest results.
flowchart TD
A["Research Goal<br/>Extend Semi-Classical Path Integral<br/>to Time-Dependent Hamiltonians<br/>for Derivatives Pricing"] --> B["Methodology<br/>Generalize Feynman-Kleinert<br/>Variational Approach"]
B --> C["Data & Inputs<br/>Black-Karasinski Model<br/>Interest Rate Dynamics<br/>Time-Dependent Parameters"]
C --> D["Computational Process<br/>1. Map Financial Hamiltonian<br/>2. Apply Semi-Classical Approx.<br/>3. Numerical Integration"]
D --> E["Key Findings / Outcomes<br/>High Accuracy vs. Analytical Benchmarks<br/>Computational Efficiency<br/>Viable Alternative to Fully-Numerical Schemes"]