Some Numerical Methods for Solving Stochastic Impulse Control in Natural Gas Storage Facilities


  • Leyla Ranjbari
  • Arifah Bahar
  • Zainal Abdul Aziz



Gas storage facility, Stochastic impulse control problems, Optimal switching, Optimal stopping time, Semi-Lagrangian scheme, HJB equation, Viscosity solution,


The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP).


A. Boogert and C. De. Jong, Gas storage valuation using a Monte Carlo method. Birkbeck Working Papers in Economics and Finance 0704, Birkbeck, School of Economics, Mathematics and Statistics. 2007.

A. Bringedal, Valuation of Gas Storage, a real options approach. NTNU. 2003.

R. Carmona and M. Ludkovski, Gas storage and supply guarantees: An optimal switching approach, Quantitative Finance, 10(4)(2010), 359-374.

Z. Chen and P. Forsyth, Implication of regime-switching model on natural gas storage valuation and optimal operation, Quantitative Finance, , 10(2)(2010), 159-176.

Z. Chen and P. Forsyth, A semi-Lagrangian approach for natural gas storage valuation and optimal operation. To appear in SIAM Journal on Scientific Computing (2006).

A. Eydeland and K. Wolyniec, Energy and Power Risk Management, New Developments in Modelling Pricing and Hedging. Wiley. 2003.

Y. He, Real options in the energy markets. Ph.D. Thesis, University of Twente, 2007.

Ranjbari et al. / Malaysian Journal of Fundamental & Applied Sciences Vol.8, No.1 (2012) 31-37.

| 37 |

S. Hikspoors and S. Jaimungal, Energy Spot Price Models and Spread Options Pricing. Commodities, Birkbeck College, University of London, 2007.

V. Kaminski, Y. Feng and Z.Pang, Value, Trading Strategies and Financial Investment of Natural Gas Storage Assets, Northern Finance Association Conference, Kananaskis, Canada. 2008.

Y. Li, Natural Gas Storage evaluation. Master’s thesis, Georgia Tech, 2006.

M. Ludkovski, Optimal switching with application to energy tolling agreements. Ph.D. Thesis, Princeton University; 2005.

M. Manoliu, Storage Options Valuation Using Multilevel Trees and Calendar Spreads.” International Journal of Theoretical and Applied Finance (2004), 425-464.

S. Nadarajah, F. Margot and N. Secomandi, Approximate dynamic programs for natural gas storage valuation based on approximate linear programming relaxations. Tepper working paper 2011-E5, 2011.

L.T. Ndounkeu, Stochastic Control: With Applications to Financial Mathematics. Ph.D. Thesis. African Institute for Mathematical Sciences (AIMS) South Africa, 2010.

C. Parsons, Quantifying natural gas storage optionality: A two-factor tree model, preprint, 2011.

D. Pilipovic, Energy Risk: Valuing and Managing Energy Derivatives. McGraw-Hill, 1997.

D. Pilipovic, Energy Risk: Valuing and Managing Energy derivatives. Second edition, McGraw-Hill, New York, 2007.

M. Thompson, M. Davison and H. Rasmussen, Natural gas storage valuation and optimization: a real options application. Working paper, University of Western Ontario, 2003.

A. Ware, Accurate semi-Lagranigian time stepping for gas storage problems. Fields Institute, University of Calgary, 2010.

A. Ware and H. Li, Natural gas storage and swing option pricing using adaptive wavelet collocation. Presented at the Oxford Centre for Industrial and Applied Mathematics Mathematical and Computational Finance Group Seminar, 2007.

W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. Springer, 2006.

H. Pham, On some recent aspects of stochastic control and their applications. Probability Surveys, 2(2005), 506–549.

Z. Chen, Numerical Methods for Optimal Stochastic Control in Finance. Ph.D. Thesis in Computer Science. University of Waterloo, Ontario, Canada, 2008.

H. Li, Adaptive wavelet collocation methods for option pricing PDEs. Ph.D. Thesis. University of Calgary, 2006.

R. Carmona and M. Ludkovski, Spot convenience yield models for the energy markets. In G. Yin and Y. Zhang, editors. AMS Mathematics of Finance, Contemporary Mathematics, 351(2004), 65-80.

H. Pham, Continuous-time stochastic control and optimization with financial applications, Springer-Verlag Berlin Heidelberg, 2009.

A. Dixit, Entry and exit decisions under uncertainty. Journal of Political Economy, 97(3)( 1989), 620–638.

A. Yushkevich, Optimal switching problem for countable Markov chains: average reward criterion. Math. Methods Oper. Res., 53(1)(2001), 1-24.