Paper: arXiv 2502.00740

Abstract

This paper examines a semi-analytical approach for pricing American options in time-inhomogeneous models characterized by negative interest rates (for equity/FX) or negative convenience yields (for commodities/cryptocurrencies). Under such conditions, exercise boundaries may exhibit a “floating” structure - dynamically appearing and disappearing. For example, a second exercise boundary could emerge within the computational domain and subsequently both could collapse, demanding specialized pricing methodologies.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly mathematical semi-analytical framework involving advanced stochastic calculus, PDE transformations, and integral equations, but lacks any empirical backtests, code, or implementation-focused validation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Pricing American options in time-inhomogeneous models with negative interest rates/convenience yields"] --> B{"Key Methodology"}
  B --> C["Semi-analytical Approach<br>Free boundary problems & valuation decomposition"]
  B --> D["Data/Inputs<br>Time-inhomogeneous parameters<br>Negative rates/convenience yields"]
  C & D --> E["Computational Process<br>Iterative solver for floating boundaries"]
  E --> F["Outcomes"]
  F --> G["Pricing function with floating boundaries"]
  F --> H["Two-boundary collapse phenomena"]
  F --> I["Equity/FX/Commodities/Crypto applications"]

Cited References (83)

  1. Semi-closed form solutions for barrier and American options written on a time-dependent Ornstein-Uhlenbeck process (2021)
  2. Closed form optimal exercise boundary of the American put option (2021)
  3. American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support (2024)
  4. Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps — → 2308.08760
  5. High-performance American option pricing (2016)
  6. Simple/Robust/Fast/Smooth Finite Difference Methods for American Options
  7. Fast American Option Pricing: The Double-Boundary Case
  8. Generalized Integral Transforms in Mathematical Finance (2021)
and 75 more
  1. Three-Month SOFR (2024) — link
  2. SOFR Derivative Pricing Using a Short Rate Model (2021) — link
  3. Trading SOFR Options (2019)
  4. SOFR Futures and Options (2022)
  5. Semi-closed form prices of barrier options in the Hull-White model (2020)
  6. Pricing Interest-Rate-Derivative Securities (1990)
  7. Interest Rate Modeling (2010)
  8. Analytic risk-free-rates option pricing with smile and skew (2023)
  9. Robust numerical methods for PDE models of Asian options (1997)
  10. A Simple Multi-Curve Model for Pricing SOFR Futures and Other Derivatives (2018) — link
  11. Finite difference scheme versus piecewise binomial lattice for interest rates under the skew CEV model (2023)
  12. The Value of an Asian Option. (1995)
  13. A P.D.E. approach to Asian options: analytical and numerical evidence (1997)
  14. Pricing arithmetic Asian and Amerasian options: A diffusion operator integral expansion approach (2023)
  15. Discounted optimal stopping for maxima in diffusion models with finite horizon (2006)
  16. Pricing of Arithmetic Average Asian Option by Combining Variance Reduction and Quasi-Monte Carlo Method (2023)
  17. Negative Interest Rates for Dummies (2020) — [link](https://derivativelogic.com/dl-report-category/negative-interest-rates-for-dummies#:~:text=Could SOFR go negative?,read that right, 0.01%.)
  18. A penalty method for American options with jump diffusion processes (2004)
  19. Computational Methods for Solving System of Volterra Integral Equation (2011)
  20. Associated Weber–Orr Transform, Bio–Savart Law and Explicit Form of the Solution of 2D Stokes System in Exterior of the Disc (2019) — link
  21. Weber’s integral Theorem (1921)
  22. Diffusion Processes with Reflection (2009)
  23. Encyclopedia of Quantitative Finance (2010)
  24. Semi-closed form prices of barrier options in the time-dependent CEV and CIR models (2020)
  25. Tata Lectures on Theta (1983)
  26. American option (2022) — link
  27. American Call Options Under Jump‐Diffusion Processes – A Fourier Transform Approach (2009)
  28. Dynamic term structure models for SOFR futures (2021)
  29. Semi-analytical pricing of options written on SOFR futures — → 2409.04903
  30. Real Options and American Derivatives: The Double Continuation Region (2015)
  31. FX Open Forward (2024)
  32. Alternative Characterizations of American Put Options (1992)
  33. Pricing American options under negative rates (2021)
  34. Bitcoin: jumps, convenience yields, and option prices (2022)
  35. Fractional cointegration in Bitcoin spot and futures markets (2021)
  36. Mathematical Models of Financial Derivatives (2008)
  37. Controlled Diffusion Processes (1980)
  38. The stochastic behavior of commodity prices: Implications for valuation and hedging (1997)
  39. The Trap of Complacency in Predicting the Maximum (2007)
  40. A Change-of-Variable Time on Curves (2005)
  41. On American VIX options under the generalized 3/2 and 1/2 models (2017)
  42. Floating exercise boundaries for American options in time-inhomogeneous models — → 2502.00740
  43. A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under Lévy Processes (2008)
  44. The H eston stochastic volatility model with piecewise constant parameters - efficient calibration and pricing of window barrier options (2018)
  45. A Change-of-Variable Formula with Local Time on Surfaces (2007)
  46. American option pricing under stochastic volatility: an efficient numerical approach (2008)
  47. Pricing American Options under Stochastic Volatility (2006)
  48. Change of Variables with Local Time on Surfaces for Jump Processes (2019) — link
  49. Predicting Functionals of Brownian Motion Through Local Time-Space Calculus (2009)
  50. Exercise boundary of the American Put near maturity in an exponential \LY model (2013)
  51. The evaluation of American option prices under stochastic volatility and jump-diffusion dynamics using the method of lines (2009)
  52. Pricing American options under stochastic volatility (2005)
  53. Limit Theorems for Stochastic Processes (1987)
  54. A survey of the integral representation of American option prices (2004)
  55. American and European options in multi-factor jump-diffusion models, near expiry (2008)
  56. Financial modelling with jump processes (2004)
  57. American and Bermudan Option Pricing by Integral Methods: the Case of Discrete Dividends. (2025)
  58. High-Performance Applications of the Non-Uniform Fast Fourier Transform to Option Pricing (2025) — link
  59. Options on realized variance by transform methods: a non-a ne stochastic volatility model (2012)
  60. Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model (2016)
  61. Pricing options on realized variance (2005)
  62. Non-Gaussian Merton-Black-Scholes Theory (2002)
  63. Estimating the parameters of 3/2 stochastic volatility model with jump (2023)
  64. Rational and Exponential Legendre Tau Method on Steady Flow of a Third Grade Fluid in a Porous Half Space
  65. On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process (2025)
  66. Some Remarks on First Passage of \LY Processes, the American Put and Pasting Principles (2005)
  67. Advances in Finance and Stochastics (2002)
  68. Some applications of \LY processes in insurance and finance (2004)
  69. The Valuation of American Options for a Class of Diffusion Processes (2002)
  70. The analytic valuation of American options (1990)
  71. An Alternative Approach to the Valuation of American Options and Applications (1996)
  72. An analysis of American options (1992)
  73. American options valuation in time-dependent jump-diffusion models via integral equations and characteristic functions — → 2506.18210
  74. American Options: Symmetry Properties (2010)
  75. Pricing and Hedging American Options: A Recursive Integration Method (1996)

4 of 83 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.