Article2007

A Semi-Lagrangian Approach for Natural Gas Storage Valuation and Optimal Operation

137 citations0/0 files storedSIAM Journal on Scientific Computing

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Adaptive Dynamic Programming Control

Abstract

The valuation of a gas storage facility is characterized as a stochastic control problem, resulting in a Hamilton–Jacobi–Bellman (HJB) equation. In this paper, we present a semi-Lagrangian method for solving the HJB equation for a typical gas storage valuation problem. The method is able to handle a wide class of spot price models that exhibit mean-reverting seasonality dynamics and price jumps. We develop fully implicit and Crank–Nicolson timestepping schemes based on a semi-Lagrangian approach and prove the convergence of fully implicit timestepping to the viscosity solution of a modified HJB equation posed on a bounded domain, provided that a strong comparison result holds. The semi-Lagrangian approach avoids Policy-type iterations required by an implicit finite difference method without requiring additional cost. Numerical experiments are presented for several variants of the basic scheme.

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References

1994Investment Under Uncertainty.2005Controlled Markov Processes and Viscosity Solutions 1996Real Options: Managerial Flexibility and Strategy in Resource Allocation 1998Derivatives: The Theory and Practice of Financial Engineering 2004Valuation of Commodity-Based Swing Options 2004Robust numerical methods for contingent claims under jump diffusion processes 2004A penalty method for American options with jump diffusion processes 2007Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance

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2008A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB)2013A Survey of Commodity Markets and Structural Models for Electricity Prices 2009Implications of a regime-switching model on natural gas storage valuation and optimal operation 2010A Hamilton–Jacobi–Bellman approach to optimal trade execution 2011Valuation of Storage at a Liquefied Natural Gas Terminal

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