Optimal Commodity Trading with a Capacitated Storage Asset

Abstract

This paper considers the so-called warehouse problem with both space and injection/withdrawal capacity limits. This is a foundational problem in the merchant management of assets for the storage of commodities, such as energy sources and natural resources. When the commodity spot price evolves according to an exogenous Markov process, this work shows that the optimal inventory-trading policy of a risk-neutral merchant is characterized by two stage and spot-price dependent basestock targets. Under some assumptions, these targets are monotone in the spot price and partition the available inventory and spot-price space in each stage into three regions, where it is, respectively, optimal to buy and inject, do nothing, and withdraw and sell. In some cases of practical importance, one can easily compute the optimal basestock targets. The structure of the optimal policy is nontrivial because in each stage the merchant's qualification of high (selling) and low (buying) commodity prices in general depends on the merchant's inventory availability. This is a consequence of the interplay between the capacity and space limits of the storage asset and brings to light the nontrivial nature of the interface between trading and operations. A computational analysis based on natural gas data shows that mismanaging this interface can yield significant value losses. Moreover, adapting the merchant's optimal trading policy to the spot-price stochastic evolution has substantial value. This value can be almost entirely generated by reacting to the unfolding of price uncertainty, that is, by sequentially reoptimizing a model that ignores this source of uncertainty.inventory, production, policies, dynamic programming, Markov, finance, asset pricing, real options, industries, petroleum, natural gas

Dynamic Risk Management of Commodity Operations: Model and Analysis

“…These papers, however, mostly deal with a situation where the markets are complete and/or the firm does not face risk costs (cases (NC), (SC) and (NI) in Table 1). Secomandi (2010) and Lai et al (2010) for instance, are papers that consider complete markets and determine the optimal operational policy for a natural gas storage facility. Goel and Gutierrez (2006) and Berling and Martínez-de Albéniz (2011) are papers where the market is incomplete, but the firm faces no significant risk costs.…”

Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage

“…However, our approach is more general than the one of LMS. We also introduce new ADPs, adding to the literature on commodity storage valuation (e.g., Chen and Forsyth 2007, Boogert and De Jong 2008, Thompson et al 2009, Carmona and Ludkovski 2010, Secomandi 2010, Wu et al 2010, Birge 2011, Boogert and De Jong 2011, and Felix and Weber 2012. More broadly, our PSR approach potentially provides a solution methodology for other real option problems.…”

Asset Pricing in Incomplete Markets: Valuing Gas Storage Capacity

“…We discuss the literature on both aspects separately. Jaillet et al [2004], Secomandi [2010] and Boogert and De Jong [2008] all assume that the underlying asset follows a mean-reversion process with constant volatility. Moreover, Thompson et al [2009] add jumps to constant volatility models.…”

“…Deviating from the above models, Boogert and De Jong [2011] and Parsons [2013] decompose the long-term and short-term behavior of the observed price dynamics and describe them separately in a two-factor model. Both Jaillet et al [2004] and Secomandi [2010] apply trinomial lattice techniques to solve for the capacity prices. However, this method suffers from the curse of dimensionality and therefore requires heavy computations.…”

“…For example, by allowing simple trading strategy for managing the storage with fixed spot price thresholds for actions including injection, withdrawal, and doing nothing, Secomandi [2010] indicates that the dynamics of stochastic spot prices have major effects on the optimal decision policies. He also emphasizes the importance of correctly modeling the uncertainty embedded in the underlying processes and shows how the valuations differ for high and low volatility assumptions.…”