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Enhancing path-integral approximation for non-linear diffusion with neural network

Anna Knezevic

TL;DR

This work tackles pricing under the Black-Karasinski short-rate model by augmenting the existing GTFK path-integral approximation with a neural network that adapts the drift- and diffusion-relevant coefficients. The neural-network component targets the function of $\bar{x}$ and the coefficients in the Taylor expansion of $e^{x}$, enabling improved calibration across varying horizons and parameter regimes. Key findings show that neural augmentation yields better long-horizon fits in regimes with pronounced interaction between mean reversion and volatility, particularly when biases are incorporated into optimisation, while some parameter couplings do not improve performance. The approach points to future extensions, including higher-dimensional (two-factor) BK models and exploration of the unconditional distribution, with practical implications for more accurate fixed-income pricing across challenging market conditions.

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.

Enhancing path-integral approximation for non-linear diffusion with neural network

TL;DR

This work tackles pricing under the Black-Karasinski short-rate model by augmenting the existing GTFK path-integral approximation with a neural network that adapts the drift- and diffusion-relevant coefficients. The neural-network component targets the function of and the coefficients in the Taylor expansion of , enabling improved calibration across varying horizons and parameter regimes. Key findings show that neural augmentation yields better long-horizon fits in regimes with pronounced interaction between mean reversion and volatility, particularly when biases are incorporated into optimisation, while some parameter couplings do not improve performance. The approach points to future extensions, including higher-dimensional (two-factor) BK models and exploration of the unconditional distribution, with practical implications for more accurate fixed-income pricing across challenging market conditions.

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.
Paper Structure (13 sections, 5 equations, 3 figures)

This paper contains 13 sections, 5 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background- literature review
  3. Structure of the paper
  4. Existing GTFK approximation
  5. Basic definitions
  6. Model formulation - Neural Network
  7. Neural Network Specification
  8. Conclusion
  9. Additional findings and further work
  10. Appendix 1
  11. Disclosure of interest
  12. Declaration of funding
  13. Data availability statement

Figures (3)

  • Figure 1: Average sensitivity of error relative to simulations, across non-training calibrations pre optimisation
  • Figure 2: Average sensitivity of error relative to simulations, across non-training calibrations post optimisation
  • Figure 3: Density of the improved predictions along $\alpha$ (y-axis) and $\sigma$ (x-axis)