Paper: arXiv 2408.02064

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

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0 of 77 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.