Black-Karasinski Model

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. ...

Enhancing path-integral approximation for non-linear diffusion with neural network ArXiv ID: 2404.08903 “View on arXiv” Authors: Unknown Abstract Enhancing the existing solution for pricing of fixed income instruments within Black-Karasinski model structure, with neural network at various parameterisation points to demonstrate that the method is able to achieve superior outcomes for multiple calibrations across extended projection horizons. Keywords: Black-Karasinski Model, Fixed Income Pricing, Neural Networks, Interest Rate Models, Fixed Income Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper employs advanced mathematical concepts including path integrals, Taylor series expansions, and PDE approximations, but lacks empirical validation with backtests or statistical metrics, focusing instead on theoretical model formulation. flowchart TD A["Research Goal"] --> B["Data & Calibration"] A --> C["Methodology"] B --> D["Path-Integral Approx."] C --> D D --> E["Neural Network Enh."] E --> F["Computational Process"] F --> G["Key Outcomes"] subgraph Inputs A B C end subgraph Processing D E F end subgraph Results G end