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**Numerical methods for the pricing of swing options: a stochastic control approach.**
*(English)*
Zbl 1142.91502

Summary: 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.

### MSC:

91G60 | Numerical methods (including Monte Carlo methods) |

93E03 | Stochastic systems in control theory (general) |

### Keywords:

swing options; Monte Carlo simulations; bang-bang control; parametric consumption; stochastic gradient
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\textit{C. Barrera-Esteve} et al., Methodol. Comput. Appl. Probab. 8, No. 4, 517--540 (2006; Zbl 1142.91502)

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