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2023 | OriginalPaper | Chapter

3. Fundamentals, Storage, and the Model of the Squeeze

Author : Ilia Bouchouev

Published in: Virtual Barrels

Publisher: Springer Nature Switzerland

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Abstract

We use the conventional storage theory to illustrate the dynamic feedback loop between prices and inventories and highlight the challenge of its practical applications to the oil market. We then borrow some concepts from the physics of extreme events and develop a more practical alternative approach to the storage problem. We call it a stylized model of the squeeze. For an example of such a squeeze, we delve into the infamous episode of negative oil prices.

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Footnotes
1
Working’s original observations on commodity storage were published between 1929 and 1933 in a series of short articles issued by Wheat Studies of the Food Research Institute. The more complete version of his argument is summarized in Working (1948) and Working (1949). The approach was further extended by Brennan (1958).
 
2
For simplicity, we use the terms convenience benefits and convenience yield interchangeably and refer to the previous chapter for their definitions.
 
3
The theory of storage was pioneered by Gustafson (1958) and subsequently extended in multiple directions. The formulation that we present here is largely based on the ideas of Deaton and Laroque (1992). This method has been applied to the oil market by Dvir and Rogoff (2009). For other related methods of solving this problem, see Williams and Wright (1991), Routledge et al. (2000), and Pirrong (2012).
 
4
More formally, the price elasticity of demand is defined as \( e=\frac{dD/D}{dS/S} \). While it is difficult to measure this elasticity precisely, it has been steadily declining over time, as increasing overall wealth made consumers less sensitive to energy prices. See, for example, Hamilton (2009) and Kilian (2020).
 
5
The assumption that the futures price is equal to the expected spot price implies that the futures price is fair and unbiased. It is equivalent to the so-called risk-neutral pricing that we will formally introduce in later chapters. In the next chapter, we also consider the case when futures price differs from the expected spot price, as futures may be distorted by imbalances in the hedging market.
 
6
Brennan and Schwartz (1985) applied a one-factor lognormal model for the spot price with deterministic convenience yield to derive futures prices. The model was further extended in Brennan (1991). One-factor models, however, have quickly proven to be too restrictive, as they allow futures across all maturities to move only in the same direction. A popular two-factor model of Gibson and Schwartz (1990), which assumes a stochastic mean-reverting convenience yield, generates a much richer dynamics for the futures curve and volatilities. Miltersen (2003) allowed the equilibrium convenience yield to be time-dependent and showed how to make the model consistent with the futures curve. Several three-factor models have been proposed, such as Schwartz (1997), Casassus and Collin-Dufresne (2005), and Dempster et al. (2012). For surveys of reduced-form models, we refer to Clewlow and Strickland (2000), Eydeland and Wolyniec (2003), and Carmona and Ludkovski (2004).
 
7
In Bouchouev (2021), the author applied a slightly different methodology to this problem by representing the futures spread as the solution to the Black-Scholes-Merton (BSM) partial differential equation, where inventory is a state variable. Here, we use a somewhat simplified approach, as BSM equation is formally introduced only later, in Chap. 8.
 
8
Some storage was already committed but not yet reflected in inventory data, nevertheless, even including these additional volumes, the total inventory levels were substantially below the maximum operating capacity.
 
9
For additional discussions of the episode of negative prices, see Interim Stuff Report (2020), Bouchouev (2020), Fernandez-Perez et al. (2021), and Ma (2022).
 
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Metadata
Title
Fundamentals, Storage, and the Model of the Squeeze
Author
Ilia Bouchouev
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-36151-7_3