Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach
Christophe Barrera-Esteve (),
Florent Bergeret (),
Charles Dossal (),
Emmanuel Gobet (),
Asma Meziou (),
Rémi Munos () and
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Christophe Barrera-Esteve: Gaz de France - Direction de la Recherche
Florent Bergeret: Gaz de France
Charles Dossal: Ecole Polytechnique, Centre de Mathématiques Appliquées
Emmanuel Gobet: ENSIMAG - INP Grenoble - Laboratoire de Modélisation et Calcul
Asma Meziou: Ecole Polytechnique, Centre de Mathématiques Appliquées
Rémi Munos: Ecole Polytechnique, Centre de Mathématiques Appliquées
Damien Reboul-Salze: Gaz de France
Methodology and Computing in Applied Probability, 2006, vol. 8, issue 4, 517-540
Abstract In the natural gas market, many derivative contracts have a large degree of flexibility. These are known as Swing or Take-Or-Pay options. They allow their owner to purchase gas daily, at a fixed price and according to a volume of their choice. Daily, monthly and/or annual constraints on the purchased volume are usually incorporated. Thus, the valuation of such contracts is related to a stochastic control problem, which we solve in this paper using new numerical methods. Firstly, we extend the Longstaff–Schwarz methodology (originally used for Bermuda options) to our case. Secondly, we propose two efficient parameterizations of the gas consumption, one is based on neural networks and the other on finite elements. It allows us to derive a local optimal consumption law using a stochastic gradient ascent. Numerical experiments illustrate the efficiency of these approaches. Furthermore, we show that the optimal purchase is of bang-bang type.
Keywords: Swing options; Monte Carlo simulations; Bang-bang control; Parametric consumption; Stochastic gradient; 90C31; 91B02; 93Exx (search for similar items in EconPapers)
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