Gas Storage and Supply Guarantees : An Optimal Switching Approach

We consider the valuation of gas storage on finite horizon. Focusing on the timing optionality of storage we construct a stochastic control model that reduces to solving an optimal switching problem with inventory. Extending the methodology from Carmona and Ludkovski (2005), we then construct a robust numerical scheme based on Monte Carlo regressions. The idea is to simultaneously approximate the optimal switching times along all the simulated paths. The main difficulty is dealing with the path-dependent inventory. The scheme is compared to the traditional quasi-variational framework and illustrated with a variety of concrete examples. We also consider related problems of interest, such as supply guarantees and natural resource management.

[1]  Kim G. Larsen,et al.  To Store or Not to Store , 2003, CAV.

[2]  John N. Tsitsiklis,et al.  Regression methods for pricing complex American-style options , 2001, IEEE Trans. Neural Networks.

[3]  Agnès Sulem,et al.  Time-to-build and capacity choice , 2002 .

[4]  Mihail Zervos,et al.  A Problem of Sequential Entry and Exit Decisions Combined with Discretionary Stopping , 2003, SIAM J. Control. Optim..

[5]  P. Wilmott,et al.  The Mathematics of Financial Derivatives: Contents , 1995 .

[6]  Michael Ludkovski,et al.  Optimal Switching with Applications to Energy Tolling Agreements , 2005 .

[7]  Margaret C. Insley On the Option to Invest in Pollution Control Under a Regime of Tradable Emissions Allowances , 2003 .

[8]  Monique Jeanblanc,et al.  On the Starting and Stopping Problem: Application in Reversible Investments , 2007, Math. Oper. Res..

[9]  Alain Bensoussan,et al.  Impulse Control and Quasi-Variational Inequalities , 1984 .

[10]  D. McNickle,et al.  The Incorporation of Hydro Storage into a Spot Price Model for the New Zealand Electricity Market , 2004 .

[11]  Eduardo S. Schwartz,et al.  Evaluating Natural Resource Investments , 1985 .

[12]  A. Dixit Entry and Exit Decisions under Uncertainty , 1989, Journal of Political Economy.

[13]  B. Øksendal,et al.  Optimal Switching in an Economic Activity Under Uncertainty , 1994 .

[14]  E. Prescott,et al.  Investment Under Uncertainty , 1971 .

[15]  René Carmona,et al.  Pricing and Hedging Spread Options , 2003, SIAM Rev..

[16]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[17]  Martin B. Haugh,et al.  Pricing American Options: A Duality Approach , 2001, Oper. Res..

[18]  A. Eydeland,et al.  Energy and Power Risk Management: New Developments in Modeling, Pricing, and Hedging , 2002 .