Pricing American Commodity Options Under the Schwartz Two-Factor Model Using the Alternating Direction Explicit (ADE) Method

By Sanjith Prabhu, Daniel J. Duffy

Rating

1805
Battle Count: 50

Relevance

8/10
Highly relevant for quantitative analysts and traders in the commodity sector. It provides an efficient numerical method for pricing complex American options, which are common in commodity markets, and offers insights into hedging with two-factor Greeks.

Implementation Complexity

7/10
Implementing the ADE scheme requires careful handling of the cross-derivative term, boundary conditions via Fichera theory, and the projection step for American exercise. The C++ implementation described is modular but requires strong numerical analysis skills.

Reproducibility

3/5
The paper provides detailed mathematical derivations, parameter sets (WTI crude oil from Schwartz 1997), and algorithmic steps. It mentions an accompanying source file and C++ implementation following Duffy (2004), but no public GitHub URL is explicitly provided in the text extract. The simulation parameters are fully specified, allowing for re-implementation.

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.

Links

arXiv:2610.21145 ยท Paper rankings

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