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"]