Paper: arXiv 2603.12375

Authors: Kevin Mott

Abstract

This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional numerical methods computationally prohibitive. To make the problem computationally tractable, I cast the stochastic pricing problem as a deterministic partial differential equation (PDE). Finance-Informed Neural Networks (FINNs) solve this PDE directly by minimizing violations of the differential equation and boundary condition, with automatic differentiation efficiently computing the exact derivatives needed to evaluate PDE terms. FINNs achieve pricing accuracy within 0.04 to 0.07 cents per dollar of contract value compared to Monte Carlo benchmarks. Once trained, FINNs price caplets in a few microseconds regardless of dimension, delivering speedups ranging from 300,000 to 4.5 million times faster than Monte Carlo simulation as the state space discretization of the forward curve grows from 10 to 150 nodes. The major Greeks-theta and curve deltas-come for free, computed automatically during PDE evaluation at zero marginal cost, whereas Monte Carlo requires complete re-simulation for each sensitivity. The framework generalizes naturally beyond caplets to other path-dependent derivatives-caps, swaptions, callable bonds-requiring only boundary condition modifications while retaining the same core PDE structure.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical fusion of the Heath-Jarrow-Morton framework with Feynman-Kac PDEs and deep learning (FINNs) to bypass high-dimensional Monte Carlo simulations. It offers high math complexity alongside detailed benchmarking of computational speedups and pricing errors, though public code links are omitted in the text.

Research Flowchart

  flowchart TD
    A[Goal: Fast, Arbitrage-Free Pricing of Path-Dependent Interest Rate Derivatives] --> B[Inputs: HJM Forward Curve Model, Contract Payoffs & Boundary Conditions]
    B --> C[Methodology: Cast Infinite-Dim Stochastic Model into Deterministic PDE]
    C --> D[Model Training: Finance-Informed Neural Networks FINNs via Automatic Differentiation]
    D --> E[Key Outcomes: <br>- Accuracy: Within 0.04-0.07¢ per dollar vs Monte Carlo<br>- Speedup: 300,000x to 4.5MX faster <br>- Greeks: Free computation of Theta & Curve Deltas<br>- Generalizability: Easily extends to Caps, Swaptions & Callable Bonds]

Cited References (112)

  1. An exact consumption-loan model of interest with or without the social contrivance of money (1958)
  2. Existence and local uniqueness of functional rational expectations equilibria in dynamic economic models (1988)
  3. Stationary Markov Equilibria (1994)
  4. Recursive Equilibrium in Stochastic Overlapping Generations Economies (2010)
  5. Markov rational expectations equilibria in an overlapping generations model (1986)
  6. Trends in College Pricing and Student Aid 2021 (2021)
  7. The capital asset pricing model as a general equilibrium with incomplete markets (1990)
  8. The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds (1970)
and 104 more
  1. Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies (2012)
  2. Short-memory equilibrium in stochastic overlapping generations economies (2007)
  3. White House officials weigh income limits for student loan forgiveness (2022) — link
  4. Putting student loan forgiveness in perspective: How costly is it and who benefits? (2022) — link
  5. Income and wealth heterogeneity in the macroeconomy (1998)
  6. Deep learning for solving dynamic economic models. (2021)
  7. Deep equilibrium nets (2019)
  8. Asset pricing with idiosyncratic risk and overlapping generations (2007)
  9. Do sunspots matter? (1983)
  10. Approximation by superpositions of a sigmoidal function (1989)
  11. The distributional effects of student loan forgiveness (2023)
  12. Human capital and growth: Theory and evidence (1989)
  13. DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks (2021) — link
  14. Student Loans Owned and Securitized (SLOAS) (2022) — link
  15. Market capitalization of listed domestic companies (current US$) - United States (2022) — link
  16. Credit constraints in education (2011)
  17. Estimation of educational borrowing constraints using returns to schooling (2004)
  18. FACT SHEET: President Biden Announces Student Loan Relief for Borrowers Who Need It Most (2022) — link
  19. Junior can’t borrow: A new perspective on the equity premium puzzle (2002)
  20. Adam: A method for stochastic optimization (2014) — link
  21. Time-inconsistent preferences, investment and asset pricing (2016) — link
  22. Quasi-hyperbolic discounting and the existence of time-inconsistent retirement (2013)
  23. Equilibrium Analysis in Behavioral One-Sector Growth Models (2020)
  24. Student Debt and Labor Market Trajectories (2022)
  25. Serenity Now, Save Later? Evidence on Retirement Savings Puzzles from a 401 (k) Field Experiment (2022)
  26. Present bias and financial behavior (2019) — link
  27. Hyperbolic discount functions, undersaving, and savings policy (1996)
  28. Simple Allocation Rules and Optimal Portfolio Choice Over the Lifecycle (2021) — link
  29. The Foundation of Target-Date Funds and Annuities (2017)
  30. Intergenerational risk-sharing via social security when financial markets are incomplete (2002)
  31. Inflation and the redistribution of nominal wealth (2006)
  32. Aggregate and welfare effects of redistribution of wealth under inflation and price-level targeting (2010)
  33. Generational risk-is it a big deal?: Simulating an 80-period olg model with aggregate shocks (2013)
  34. Intergenerational risk sharing in the spirit of Arrow, Debreu, and Rawls, with applications to social security design (2007)
  35. How America Saves 2022 (2022)
  36. Optimal portfolio choice with wage-indexed social security (2011)
  37. Restoring rational choice: The challenge of consumer financial regulation (2016)
  38. Intergenerational Redistribution in the Great Recession (2020) — link
  39. A class of smoothing functions for nonlinear and mixed complementarity problems (1994)
  40. Borrowing Costs and the Equity Premium in Standard OLG Models (2015)
  41. Tuition, debt, and human capital (2020)
  42. Student loans and borrower outcomes (2022)
  43. Student Debt and Entrepreneurship in the US (2022)
  44. Are they all like Bill, Mark, and Steve? The education premium for entrepreneurs (2020)
  45. Schooling, capital constraints, and entrepreneurial performance: The endogenous triangle (2006)
  46. Estimating Nonlinear Heterogeneous Agents Models with Neural Networks (2022)
  47. Before and After Target Date Investing: The General Equilibrium Implications of Retirement Savings Dynamics (2022)
  48. A dynamic Nelson-Siegel yield curve model with Markov switching (2017)
  49. Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation (1992)
  50. Markov representation of the Heath-Jarrow-Morton model (2001)
  51. Feynman-Kac theorem in Hilbert spaces (2014) — link
  52. How Do Tax Incentives Influence Employer Decisions to Offer Retirement Benefits? (2025) — link
  53. Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994 (1994) — link
  54. The US Treasury yield curve: 1961 to the present (2007)
  55. Martingale Methods in Financial Modelling (2005) — link
  56. A penalized Fischer-Burmeister NCP-function (2000)
  57. Tobin’s marginal q and average q: A neoclassical interpretation (1982)
  58. College Loans and Human Capital Investment (2025) — link
  59. Implications of security market data for models of dynamic economies (1991)
  60. Intergenerational consequences of rare disasters (2024)
  61. Deep Learning for Solving Economic Models (2025) — link
  62. Survey of Consumer Finances, 2019 (2019) — link
  63. Aliens and continuous time economies (2021)
  64. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (2019)
  65. A general equilibrium approach to monetary theory (1969)
  66. Capital theory and investment behavior (1963)
  67. The federal student loan program: Quantitative implications for college enrollment and default rates (2009)
  68. The nature of credit constraints and human capital (2011)
  69. Education policy and intergenerational transfers in equilibrium (2019)
  70. Evaluating fiscal policy with a dynamic simulation model (1987)
  71. Young, old, conservative, and bold: The implications of heterogeneity and finite lives for asset pricing (2015)
  72. Demography and the long-run predictability of the stock market (2004)
  73. “No One Can Borrow”–Reassessing the “Junior Can’t Borrow” Equity-Premium Puzzle Resolution (2025)
  74. Essays on Overlapping Generations Models and Social Security (2021)
  75. Preference Heterogeneity, Aggregate Risk and the Welfare Effects of Social Security (2018)
  76. Optimal asset location and allocation with taxable and tax-deferred investing (2004)
  77. Retirement financing: An optimal reform approach (2019)
  78. An equilibrium characterization of the term structure (1977)
  79. A theory of the term structure of interest rates (1985)
  80. Pricing interest-rate-derivative securities (1990)
  81. The market model of interest rate dynamics (1997)
  82. The pricing of commodity contracts (1976)
  83. The pricing of options and corporate liabilities (1973)
  84. Theory of rational option pricing (1971)
  85. A Variational Autoencoder Approach to Conditional Generation of Possible Future Volatility Surfaces (2023)
  86. Hedging Barrier Options Using Reinforcement Learning (2024)
  87. Gamma and vega hedging using deep distributional reinforcement learning (2023)
  88. Deep learning for exotic option valuation (2021) — link
  89. A neural network approach to understanding implied volatility movements (2020)
  90. Solving high-dimensional partial differential equations using deep learning (2018)
  91. DGM: A deep learning algorithm for solving partial differential equations (2018)
  92. Solving the Kolmogorov PDE by means of deep learning (2021)
  93. Stochastic calculus for finance II: Continuous-time models (2004)
  94. Plan design and participant behavior in defined contribution retirement plans: Past, present, and future (2024)
  95. Pension substitution in the 1980s: Why the shift toward defined contribution? (1995)
  96. The evolution of us firms’ retirement plan offerings: Evidence from a new panel data set (2021)
  97. Aggregate implications of defined benefit and defined contribution systems (2003)
  98. Asset Pricing and Risk-Sharing Implications of Alternative Pension Plan Systems (2023)
  99. Optimal savings with taxable and tax-deferred accounts (2009)
  100. Borrow now, pay even later: A quantitative analysis of student debt payment plans (2024)
  101. Differential machine learning (2020) — link
  102. Differential ML with a Difference (2025) — link
  103. Deep hedging (2019) — link
  104. Machine learning methods for pricing financial derivatives — → 2406.00459

1 of 112 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.