Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.21145

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

Sanjith Prabhu·Daniel J. Duffy
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

q-fin.CP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sanjith Prabhu, Daniel J. Duffy. 2026-10-15. Pricing American Commodity Options Under the Schwartz Two-Factor Model Using the Alternating Direction Explicit (ADE) Method. https://arxiv.org/abs/2610.21145

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Global Multi-Maturity SPX-VIX Calibration Beyond Markovian Stitching

We develop a global martingale optimal transport framework for joint S&P 500 (SPX)-VIX smile calibration across multiple maturities, without the conditional independence that Markovian stitching imposes between months. We prove that exact local and global feasibility are equivalent, yet the stitched laws, which carry earlier months only through the current SPX level, can form a strict subset of the global ones, so adjacent smiles cannot identify the dependence across months. We show that relative entropy against the standard Markov reference selects the stitched law, so this dependence must be supplied deliberately. We supply it through a finite-memory reference, in which a latent autoregressive state drives the VIX levels while every VIX marginal stays exact, and calibrate the resulting law on a junction tree whose size grows linearly with the number of maturities. On market data with up to nine SPX maturities, a law with memory and a law without it fit the same quotes but price VIX-conditioned SPX Asian claims differently: on every calendar, memory makes a claim on the maximum VIX cheaper and a claim on the minimum VIX dearer. Varying the memory strength on one calendar moves these differences steadily from zero, so the vanilla quotes, which fix the law of each date, do not determine prices that depend on the joint law across dates.

q-fin.CP↗
arXiv2026

Algorithmic Collusion Without Deterrence: Auditing the Punishment Mechanism in Q-Learning Pricing Agents

Independent tabular Q-learning agents repricing in a simulated Bertrand duopoly converge to supracompetitive prices, and the seminal evidence attributes this to a learned reward-punishment scheme: undercut your rival and it retaliates, so deviation never pays. This mechanistic reading is what turns high prices into a cartel, and into a regulatory target. We replicate the environment of Calvano et al. (2020) and confirm their impulse-response pattern within co-trained pairs. We then audit the pattern on frozen policies, with learning off, and find that on its own it does not identify a mechanism: the return is over-determined rather than selective. In nine of ten converged pairs (914 of 1,024) a single attractor's basin is the entire state space, so every perturbation returns whatever provoked it, and a forced price increase triggers the same retaliatory pattern as an undercut. What co-training produces is a narrow, dyad-specific basin of attraction: re-match frozen agents from independent runs, as Calvano et al. did with learning on, and coordination collapses by 80% with nothing carried across. The deterrence claim is incomplete on its own terms: the one-period undercut of Calvano et al.'s impulse-response test is unprofitable, which we confirm in 92% of pairs, but the optimal deviation, computed by dynamic programming against each partner's frozen strategy, profits by 17.5% on average. The scheme deters only the deviation no optimizer would choose; collusion survives because deviation is never tried, not because it would not pay. Supracompetitive prices are robust; the punishment mechanism read into them does not survive these tests, which changes what the standard test of algorithmic collusion establishes, and what pairing-disruption remedies can be expected to do.

q-fin.CP↗
arXiv2026

When Does "Post-Call" Begin? An Availability Contract for Earnings-Call NLP Benchmarks

Corporate financial disclosures often unfold over time, with announcements, prepared remarks, and discussion spanning multiple high-frequency return intervals. Financial NLP benchmarks can therefore suffer from a within-event timing mismatch when the prediction target begins before the textual or audio input used by a model could be complete. Chronological train--test splits do not prevent this mismatch, because it occurs inside individual events rather than across samples. We introduce an Availability Contract, which requires a benchmark to state the input boundary, evidence for input availability, the outcome start, and the claims supported by that evidence. We apply this framework to 552 earnings calls from 24 firms. For each call, we hold the return endpoint fixed and compare the previous close, a documentary call-start proxy, and a completion proxy based on reconstructed audio end plus a stipulated processing allowance. At this baseline, moving from the call-start proxy to the completion proxy flips return signs for 9.4% of calls. Holding completion-clock cutpoints fixed, 28.3% change quintile. In an independent release-session analysis of a public earnings-call volatility benchmark, shifting before-market target windows forward by one trading session raises three-day mean squared error by 18.1-21.4% across four frozen prediction streams, while their point rankings remain unchanged. Together, the results show that labels and losses can depend materially on the declared outcome clock even when model rankings appear stable. The Availability Contract makes this assumption explicit and ties post-input claims to the available timing evidence.

q-fin.CP↗