Pricing American Commodity Options Under the Schwartz Two-Factor Model Using ADE
ORIGINAL / Pricing American Commodity Options Under the Schwartz Two-Factor Model Using the Alternating Direction Explicit (ADE) Method
This study applies the double-sweep Alternating Direction Explicit (ADE) method to price American commodity options under the Schwartz two-factor model and compares it with Saul'yev's single-sweep variant; its value lies in an unconditionally stable (for diffusion) finite difference scheme with explicit marching efficiency, extended to exercise on futures prices and seasonal parameters.
01 ABSTRACT
The study solves American commodity option prices under the Schwartz two-factor model using a double-sweep ADE finite difference method and compares it with Saul'yev's single-sweep alternating variant. The authors derive the governing PDE, transform the semi-infinite domain into a rectangular computational domain, and apply Fichera theory to determine boundary conditions at the spot price limits. Numerical experiments first validate against the closed-form European solution and Monte Carlo, then impose the American early exercise constraint and benchmark accuracy and convergence against Longstaff-Schwartz Monte Carlo.
02 KEY FINDINGS
- The double-sweep ADE method is unconditionally stable for diffusion and combines explicit marching efficiency with implicit-like stability.
- Fichera theory is used to determine boundary conditions at spot price limits, and the semi-infinite domain is transformed into a rectangular computational domain.
- A C++ implementation is validated against the closed-form European solution and Monte Carlo, then compared with Longstaff-Schwartz Monte Carlo for American option accuracy and convergence.
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