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Optimal Operating Strategy for a Storage Facility

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Optimal Operating Strategy for a Storage Facility Optimal Operating Strategy for a Storage Facility by E Ning Zhai SEP 0 5 2008 B.Eng., Electrical Engineering LIBRARIES National University of Singapore, 2007 Submitted to the School of Engineering in Partial Fulfillment of the Requirements for the Degree of Master of Science in Computation for Design and Optimization at the Massachusetts Institute of Technology SEPTEMBER 2008 0 2008 Massachusetts Institute of Technology All rights reserved I A Signature of Author ................................... ....................... School of Engineering August 14, 2008 Certified by ............ 7 .. Jo.. ......... John E. Parso ns Senior Lecturer, Sloan School of Management, Executive Director, MIT Center for Energy and Environmental Policy Research Thesis Supervisor A ccepted by ................ r ................... f ......... ................................................................. Robert M. Freund Professor in Management Science, Sloan School of Management, Codirector, Computation for Design and Optimization Program BARKER 2 Optimal Operating Strategy for a Storage Facility by Ning Zhai B.Eng., Electrical Engineering National University of Singapore, 2007 Submitted to the School of Engineering in Partial Fulfillment of the Requirements for the Degree of Master of Science in Computation for Design and Optimization ABSTRACT In the thesis, I derive the optimal operating strategy to maximize the value of a storage facility by exploiting the properties in the underlying natural gas spot price. To achieve the objective, I investigate the optimal operating strategy under three different spot price processes: the one-factor mean reversion price process with and without seasonal factors, the one-factor geometric Brownian motion price process with and without seasonal factors, and the two-factor short-term/long-term price process with and without seasonal factors. I prove the existence of the unique optimal trigger prices, and calculate the trigger prices under certain conditions. I also show the optimal trigger prices are the prices where the marginal revenue is equal to the marginal cost. Thus, the marginal analysis argument can be used to determine the optimal operating strategy. Once the optimal operating strategy is determined, I use it to obtain the optimal value of the storage facility in three ways: 1, using directly the net present value method; 2, solving the partial differential equations governing the value of the storage facility; 3, using the Monte Carlo method to simulate the decision making process. Issues about parameter estimations are also considered in the thesis. Thesis Supervisor: John E. Parsons Title: Executive Director, MIT Center for Energy and Environmental Policy Research 3 4 ACKNOWLEDGEMENT From knowing nothing about natural gas, to writing a thesis on natural gas, I have made it because of my thesis advisor John Parsons. His enthusiasm and inspirations have given me the confidence to tackle the problem, and his timely advice and assistance have provided me the tools to solve the problem. I have learned from him not only the academic knowledge, but the attitude towards work and towards others. I thank my thesis advisor, John Parsons. This thesis has benefited greatly from the Joint-Program students in the CEEPR lab, especially their knowledge on econometrics and energy market. I thank them for their helps. I thank my CDO-Program advisor Robert Freund, who guided me on both academics and graduate life from the beginning to the end of the master program. I thank our friendly graduate administrator Laura Koller, who trusted and helped me organize successfully many student events. I want to thank the friends I have made in MIT: the CDO students, the Ashdown friends, the Graduate Student Council friends, and the people from my weekly soccer team! Because of them, I have a fantastic year in MIT. One year in MIT has just passed, but the memory in MIT will last forever! 5 6 CONTENTS ACKNOW LEDGEM ENT....................................................................................................... 5 CONTEN TS ................................................................................................................................... 7 LIST OF FIGU RES ...................................................................................................................... 9 LIST OF TABLES ...................................................................................................................... 10 LIST OF NO TATIONS .............................................................................................................. 11 CHAPTER 1 INTRODUCTION ............................................................................................ 13 1.1 Chapter Introduction........................................................................................................... 13 1.2 M otivation........................................................................................................................... 13 1.3 Literature Review ................................................................................................................ 14 1.4 Contributions....................................................................................................................... 16 1.5 Organization of the Thesis.............................................................................................. 17 CHAPTER 2 ONE-FACTOR MEAN REVERSION MODELS.................... 19 2.1 Chapter Introduction ........................................................................................................... 19 2.2 Determ inistic M odel without Seasonality........................................................................ 20 2.2.1 Scenario One - Independent Cost Rate ..................................................................... 20 2.2.2 Scenario Two - Proportionate Cost Rate................................................................. 28 2.3 Stochastic M odel without Seasonality............................................................................ 30 2.3.1 Operating Strategies with Infinite Facility Life ....................................................... 31 2.3.2 Optim al Operating Strategies with Finite Facility Life ............................................ 43 2.3.3 A Numerical Example to Find the Value of a Storage Facility ............................... 47 2.4 Seasonal Factors.................................................................................................................. 50 2.5 Determ inistic M odel with Seasonality............................................................................ 53 2.6 Stochastic M odel with Seasonality .................................................................................. 55 2.7 Value Decomposition.......................................................................................................... 57 CHAPTER 3 ONE-FACTOR GEOMETRIC BROWNIAN MOTION MODELS ...... 59 3.1 Chapter Introduction ....................................................................................................... 59 7 3.2 D eterm inistic M odel w ithout Seasonality........................................................................ 60 3.3 Stochastic M odel w ithout Seasonality............................................................................. 62 3.4 D eterm inistic M odel w ith Seasonality............................................................................. 64 3.5 Stochastic M odel w ith Seasonality ................................................................................. 64 3.6 V alue D ecom position...................................................................................................... 67 CHAPTER 4 TWO-FACTOR PRICE MODELS .................................................................. 70 4.1 Chapter Introduction ........................................................................................................... 70 4.2 Introduction to the Tw o-Factor Price M odel ................................................................... 70 4.3 V aluation U sing the Tw o-Factor Price Model................................................................. 72 4.3.1 Problem Form ulation ................................................................................................... 73 4.3.2 D erivations of the O ptim al O perating Strategies...................................................... 74 4.3.3 V aluations from the Optim al O perating Strategies...................................................... 78 4.4 V aluation w ith Seasonality ............................................................................................... 80 4.5 V alue D ecom position...................................................................................................... 81 CHAPTER 5 ESTIMATIONS FOR TWO-FACTOR MODELS................... 83 5.1 Chapter Introduction ........................................................................................................... 83 5.2 Setup of K alm an Filter...................................................................................................... 85 5.3 Param eter Estim ations ..................................................................................................... 87 5.4 A n Em pirical Example...................................................................................................... 89 CH A PTER 6 C O N C LU SIO N ................................................................................................
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