Paper: arXiv 2610.00951

Authors: Iosif Zimbidis, Ronnie Sircar

Abstract

On April 20, 2020, the May front-month WTI oil futures contract, one day before its expiration date, opened near $$17/$barrel and dropped far below zero in a single trading day, reaching an intraday low of $-$40.32$ and settling at $-$37.63$. Such market behavior was unforeseen at the time. This event, and the March 2022 nickel squeeze, illustrate how constraints on physical delivery create pressure to close futures positions and distort futures prices. We develop a feedback model that connects the resulting price distortion to a roll option, and to the imbalance between delivery-constrained long and short positions. Under lognormal benchmark dynamics, the roll-option value is shown to satisfy a pricing PDE which is nonlinear because its payoff depends on the observed futures price, which itself includes the feedback correction. Remarkably, in both cases, there is an explicit solution in terms of classical Black-Scholes-Margrabe exchange option formulas, up to solving a scalar equation. We show this allows that prices may go negative under distortion of a positive-price lognormal model. An analogous construction applies when the lognormal base is switched to Bachelier normal dynamics. Illustrations based on WTI and nickel show the imbalance required to reproduce the extreme event prices under the benchmark assumptions.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly novel and mathematically sophisticated feedback model for extreme commodity futures prices. While the empirical validation is illustrative rather than exhaustive, the analytical tractability and explicit solutions are a significant contribution. The clarity is good given the complexity, and the model’s ability to reproduce extreme events is compelling.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain Extreme Negative Futures Prices (WTI, Nickel)] --> B{Methodology: Feedback Model for Price Distortion};
    B --> C{Inputs: Lognormal/Bachelier Benchmark Dynamics, Delivery-Constrained Long/Short Imbalance};
    C --> D{Computational Process: Pricing PDE for Roll Option with Feedback Correction};
    D --> E{Solution: Black-Scholes-Margrabe Exchange Option Formulas & Scalar Equation};
    E --> F[Outcomes: Explains Negative Prices, Quantifies Imbalance for Extreme Events, Validated with WTI & Nickel];