Paper: arXiv 2404.08903

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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

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  6. Modelling interest rates in 2014 — link
  7. Stochastic Control for Asset Management (2013) — link
  8. A path-integral approximation for non-linear diffusions (2020)
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  2. Neural networks, approximation theory, and finite precision computation (1995)
  3. Approximations Of Bond And Swaption Prices In A Black–Karasi 'n ski Model (2016)
  4. General short-rate analytics (2011)
  5. An effective approximation for zero-coupon bonds and Arrow–Debreu prices in the Black–Karasinski model (2014)
  6. A closed-form approximation of likelihood functions for discretely sampled diffusions: The exponent expansion (2007)
  7. Exact arrow-debreu pricing for the black-karasinski short rate model (2019)
  8. The Black-Karasinski Model: Thirty Years On (2021)
  9. Two-Factor Black-Karasinski Pricing Kernel (2019)
  10. Invariant approaches for the analytic solution of the stochastic Black-Derman toy model (2018)
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  15. Numerical procedures for implementing term structure models II: Two-factor models (1994)
  16. Neural taylor approximations: Convergence and exploration in rectifier networks (2017)
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  18. Interest Rate Models: Paradigm shifts in recent years (2007)
  19. An empirical comparison of forward-rate and spot-rate models for valuing interest-rate options (1999)
  20. Connectionist learning procedures. Artificial Intelligence, 40 1-3: 185 234, 1989. Reprinted in J. Carbonell, editor," (1990)
  21. Scikit-learn: Machine Learning in P ython (2011)
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  23. An introduction to numerical methods for stochastic differential equations (1999)
  24. A Two-Factor Black-Karasinski Sovereign Credit Default Swap Pricing Model. (2007)
  25. Bond and option pricing when short rates are lognormal (1991)
  26. Stochastic Gradient Descent (2010)
  27. Binomial term structure models (1998)

0 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.