Paper: arXiv 2610.21145

Authors: Sanjith Prabhu, Daniel J. Duffy

Abstract

This project investigates the valuation of American commodity options using the Schwartz two-factor model. We employ the double-sweep Alternating Direction Explicit (ADE) method, an unconditionally stable (for diffusion) finite difference scheme that provides the efficiency of explicit marching with the stability typically reserved for implicit methods, and compare it with the single-sweep alternating variant of Saul’yev. We derive the governing partial differential equation (PDE) and transform the semi-infinite domain into a rectangular computational domain. Furthermore, we apply Fichera theory to determine boundary conditions at the limits of the spot price. Finally, we implement the solver in C++, validating the results first against the closed-form solution of the PDE and Monte Carlo as a European option, then apply the American early exercise constraint and benchmark against Longstaff-Schwartz Monte Carlo to analyze numerical accuracy and convergence. The framework is then extended, following feedback from a commodities trader to exercise on futures prices and use seasonal parameters.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper demonstrates a high level of mathematical sophistication in deriving and transforming the PDE, coupled with robust empirical validation against established benchmarks. The application of the ADE method to American commodity options under the Schwartz model, with practical extensions, shows strong rigor and novelty.

Research Flowchart

  flowchart TD
    A[Research Goal: Value American Commodity Options] --> B{Methodology: Schwartz Two-Factor Model};
    B --> C{Numerical Approach: Alternating Direction Explicit (ADE) Method};
    C --> D{Computational Steps: PDE Derivation & Domain Transformation, Fichera Boundary Conditions, C++ Implementation};
    D --> E{Validation & Benchmarking: Closed-form, Monte Carlo (European), Longstaff-Schwartz (American)};
    E --> F{Extension: Futures Exercise & Seasonal Parameters};
    F --> G[Outcomes: Validated & Extended Framework for American Option Pricing];