Optimal Quantization for the Pricing of Swing Options

In this paper we investigate a numerical algorithm for the pricing of swing options, relying on the so‐called optimal quantization method. The numerical procedure is described in detail and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff–Schwartz algorithm.

[1]  G. Pagès,et al.  A quantization algorithm for solving multi-dimensional Optimal Stopping problems , 2007 .

[2]  Edward C. Waymire,et al.  A self-similar invariance of critical binary Galton-Watson trees , 2000 .

[3]  R. Carmona,et al.  OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS , 2008 .

[4]  Philip Protter,et al.  An analysis of a least squares regression method for American option pricing , 2002, Finance Stochastics.

[5]  Martina Wilhelm,et al.  Finite element valuation of swing options , 2008 .

[6]  Rémi Munos,et al.  Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach , 2006 .

[7]  Juri Hinz,et al.  Valuing virtual production capacities on flow commodities , 2006, Math. Methods Oper. Res..

[8]  Patrick Jaillet,et al.  Valuation of Commodity-Based Swing Options , 2004, Manag. Sci..

[9]  Jérôme Barraquand,et al.  Numerical Valuation of High Dimensional Multivariate American Securities , 1995, Journal of Financial and Quantitative Analysis.

[10]  René Carmona,et al.  Optimal Multiple Stopping of Linear Diffusions , 2008, Math. Oper. Res..

[11]  S. Graf,et al.  Foundations of Quantization for Probability Distributions , 2000 .

[12]  G. Pagès,et al.  Optimal quantization methods and applications to numerical problems in finance , 2004 .

[13]  A. Eydeland.  Energy and Power Risk Management , 2002 .

[14]  Gilles Pagès,et al.  Optimal quadratic quantization for numerics: the Gaussian case , 2003, Monte Carlo Methods Appl..

[15]  René Carmona,et al.  Gas Storage and Supply Guarantees : An Optimal Switching Approach , 2005 .

[16]  G. Pagès,et al.  Error analysis of the optimal quantization algorithm for obstacle problems , 2003 .

[17]  Sheldon M. Ross,et al.  ON THE STRUCTURE OF A SWING CONTRACT'S OPTIMAL VALUE AND OPTIMAL STRATEGY , 2008 .

[18]  A. Lari-Lavassani,et al.  A DISCRETE VALUATION OF SWING OPTIONS , 2002 .

[19]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[20]  Gillis Pagés,et al.  A space quantization method for numerical integration , 1998 .

[21]  G. Pagès,et al.  A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS , 2005 .

[22]  A. C. Thompson.  Valuation of Path-Dependent Contingent Claims with Multiple Exercise Decisions over Time: The Case of Take-or-Pay , 1995, Journal of Financial and Quantitative Analysis.

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

[24]  Zita Marossy.  Commodities and Commodity Derivatives, Modeling and Pricing for Agriculturals, Metals and Energy, Helyette Geman, Wiley Finance (2005). 416 pages, ISBN: 978-0-470-01218-5 , 2007 .

[25]  James McNames,et al.  A Fast Nearest-Neighbor Algorithm Based on a Principal Axis Search Tree , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Juri Hinz,et al.  Valuing production capacities on flow commodities , 2005 .

[27]  Vlad Bally,et al.  The central limit theorem for a nonlinear algorithm based on quantization , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[28]  Scott H. Clearwater,et al.  Swing Options: A Mechanism for Pricing Peak IT Demand , 2005 .

[29]  Harald Luschgy,et al.  Functional quantization rate and mean regularity of processes with an application to Lévy processes , 2008 .

[30]  N. Meinshausen,et al.  MONTE CARLO METHODS FOR THE VALUATION OF MULTIPLE‐EXERCISE OPTIONS , 2004 .

[31]  R. Carmona,et al.  Pricing Asset Scheduling Flexibility using Optimal Switching , 2008 .

[32]  H. Geman.  Commodities and Commodity Derivatives: Modelling and Pricing for Agriculturals, Metals and Energy , 2005 .

[33]  Gilles Pagès,et al.  A quantization tree algorithm : improvements and financial applications for swing options , 2008 .

[34]  Gilles Pages,et al.  When are Swing options bang-bang and how to use it , 2007, 0705.0466.

[35]  Savas Dayanik,et al.  OPTIMAL MULTIPLE-STOPPING OF LINEAR DIFFUSIONS AND SWING OPTIONS , 2003 .

[36]  Dr. Uwe Dörr.  Valuation of Swing Options and Examination of Exercise Strategies by Monte Carlo Techniques , 2003 .

[37]  J. Keppo.  Pricing of Electricity Swing Options , 2004 .

[38]  Paul L. Zador,et al.  Asymptotic quantization error of continuous signals and the quantization dimension , 1982, IEEE Trans. Inf. Theory.

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

[40]  Marcelo G. Figueroa.  Pricing Multiple Interruptible-Swing Contracts , 2006 .