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(LNG) Arbitrage, Intertemporal Market Equilibrium and (Political) Uncertainty

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Control Systems and Mathematical Methods in Economics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 687))

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Abstract

Since 2009, natural gas markets are characterized by large spreads in liquefied natural gas (LNG) prices between the United States (Henry hub) and Europe and Japan. Moreover these differences are forecasted to persist (at a lower level but still above transport costs) against the law of one price. This paper explores this persistence of apparent arbitrage by investigating an intertemporal competitive equilibrium under uncertainty. Investments of an individual arbitrageur must account (at least) for: (1) rational expectation that this arbitrage will be eroded over time by competitive agents’ similar investments; (2) risk of export regulations because governments may intervene and destroy this opportunity in order to protect the interest of local (i.e. U.S.) firms and consumers. The paper analyzes a corresponding stochastic and dynamic (partial) equilibrium that leads to a reduction in investments and implies persistence of apparent arbitrage. This is in line with forecasted but unexplained price differences.

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Notes

  1. 1.

    Liquefaction costs have substantially decreased over the past 10 years to below US$200 per ton of annual liquefaction capacity, US Energy Information Administration (2003).

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Acknowledgements

I acknowledge helpful discussions about the LNG market with Yuri Yegorov and Jalal Dehnavi and comments from an anonymous referee. A very first draft of the paper was presented at World Congress of the International Association of Energy Economists, June 16th–18th 2014, New York and I thank the participants for their helpful comments.

Appendix: Declining Hazard, h ′ < 0

No particular property of h was used up to Eq. (18). Specifics of h enter only with the determination of \(S\left ( T\right ) \) in (17) and then for the linear choice as in the example (8). Thus using the same example (8) with the only modification of a linearly declining hazard rate,

$$\displaystyle \begin{aligned} h=\alpha \left( 1-X\right) \end{aligned}$$

some of the explicit calculations change,

$$\displaystyle \begin{aligned} \begin{array}{rcl} \dot{F} &\displaystyle =&\displaystyle \alpha \left( 1-x_{T}\right) \left( 1-F\right) \\ &\displaystyle \Longrightarrow &\displaystyle F\left( t\right) =1-\left( 1-F_{T}\right) e^{-h\left( x_{T}\right) \left( t-T\right) }=1-\left( 1-F_{T}\right) e^{-\alpha \left( 1-x_{T}\right) \left( t-T\right) } \\ S\left( x\left( T\right) ,T\right) &\displaystyle =&\displaystyle A\left( X\left( T\right) \right) x\left( T\right) \underset{0}{\overset{\infty }{\int }}e^{-rt}\left( 1-F\left( t\right) \right) dt \\ &\displaystyle =&\displaystyle A\left( x_{T}\right) x_{T}\left( 1-F_{T}\right) \underset{0}{\overset{ \infty }{\int }}e^{-\left( r+\alpha \left( 1-x_{T}\right) \right) t}dt=\frac{ A\left( x_{T}\right) x_{T}\left( 1-F_{T}\right) }{r+\alpha \left( 1-x_{T}\right) }. \end{array} \end{aligned} $$

Reformulated as a stopping problem, the optimal stopping conditions are:

$$\displaystyle \begin{aligned} \begin{array}{rcl} \lambda \left( T\right) &\displaystyle =&\displaystyle S_{x}=\frac{A\left( x_{T}\right) \left( 1-F\right) }{r+\alpha \left( 1-x_{T}\right) } \\ H\left( T\right) &\displaystyle =&\displaystyle rS-\frac{\partial S}{\partial T} \\ \frac{\partial S}{\partial T} &\displaystyle =&\displaystyle -\frac{A\left( x_{T}\right) x_{T}}{r+\alpha \left( 1-x_{T}\right) }\frac{\partial F}{\partial T} \end{array} \end{aligned} $$
$$\displaystyle \begin{aligned} \frac{\partial F}{\partial t}=-\left( 1-F\right) \frac{\partial }{\partial t} e^{-\alpha \left( 1-x\left( T\right) \right) \left( t-T\right) }=\alpha \left( 1-X\right) \left( 1-F\right) e^{-\alpha X\left( t-T\right) }\mid _{t=T}=\alpha \left( 1-X\right) \left( 1-F\right) \end{aligned}$$
$$\displaystyle \begin{aligned}\begin{array}{rcl} H &\displaystyle =&\displaystyle A\left( X\right) x\left( 1-F\right) -k\left( u\right) +\frac{A\left( X\right) \left( 1-F\right) }{r+\alpha \left( 1-X\right) }u\text{ at }t=T, \\ rS-\frac{\partial S}{\partial T} &\displaystyle =&\displaystyle \frac{A\left( x_{T}\right) x_{T}\left( 1-F_{T}\right) r}{r+\alpha \left( 1-x_{T}\right) }+\frac{A\left( x_{T}\right) x_{T}\alpha \left( 1-X\right) \left( 1-F\right) }{r+\alpha \left( 1-x_{T}\right) } \\ &\displaystyle =&\displaystyle \frac{A\left( x_{T}\right) x_{T}\left( 1-F_{T}\right) \left( r+\alpha \left( 1-X\right) \right) }{r+\alpha \left( 1-x_{T}\right) }=Ax\left( 1-F\right) \text{ at }t=T. \end{array} \end{aligned} $$

Therefore,

$$\displaystyle \begin{aligned} Ax_{T}\left( 1-F_{T}\right) -k\left( u\right) +\frac{A\left( 1-F_{T}\right) }{r+\alpha \left( 1-X\right) }u=Ax_{T}\left( 1-F_{T}\right) \end{aligned}$$

which holds for \(u\left ( T\right ) =0\). As a consequence, the corresponding stopping condition,

$$\displaystyle \begin{aligned} \lambda \left( T\right) =\frac{A\left( x_{T}\right) \left( 1-F\right) }{ r+\alpha \left( 1-x_{T}\right) }=k^{\prime }\left( 0\right) , \end{aligned}$$

is similar

$$\displaystyle \begin{aligned} A\left( 1-F\right) =\left( r+\alpha \left( 1-x_{T}\right) \right) k. \end{aligned}$$

Figures 7 and 8 are the counterparts of Figs. 2 and 4 highlighting the similarity in spite of the opposite assumptions of either h ′ > 0 or h ′ < 0.

Fig. 7
figure 7

Counterpart of Fig. 2 for declining hazard rate, h = α(1 − x): Determination of capacity: deterministic (steady state) vs stochastic (maximum, i.e. in case of no prior intervention) for F fixed at terminal value

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Fig. 8
figure 8

Counterpart of Fig. 4 for declining hazard rate, h = α(1 − x) Time paths (assuming no intervention prior to T), reference example: α = 0.1, κ = 2, γ = 10, r = 0.1

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Authors and Affiliations

  1. University of Vienna, Faculty of Business, Economics and Statistics, Vienna, Austria

    Franz Wirl

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  1. Franz Wirl
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Correspondence to Franz Wirl .

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Editors and Affiliations

  1. Operations Research and Control Systems, Vienna University of Technology , Vienna, Austria

    Gustav Feichtinger

  2. Operations Research and Control Systems, Vienna University of Technology, Vienna, Austria

    Raimund M. Kovacevic

  3. Operations Research and Control Systems, Vienna University of Technology, Vienna, Austria

    Gernot Tragler

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Wirl, F. (2018). (LNG) Arbitrage, Intertemporal Market Equilibrium and (Political) Uncertainty. In: Feichtinger, G., Kovacevic, R., Tragler, G. (eds) Control Systems and Mathematical Methods in Economics. Lecture Notes in Economics and Mathematical Systems, vol 687. Springer, Cham. https://doi.org/10.1007/978-3-319-75169-6_12

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