Modelling spikes and pricing swing options in electricity markets.

*(English)*Zbl 1182.91176Summary: Most electricity markets exhibit high volatilities and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. In this paper we examine a simple spot price model that is the exponential of the sum of an Ornstein-Uhlenbeck and an independent mean-reverting pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of the spot price process at maturity \(T\). Hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulae for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilized which in turn uses approximations to the conditional density of the spot process.

##### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

91G80 | Financial applications of other theories |

60J75 | Jump processes (MSC2010) |

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

##### Keywords:

energy derivatives; financial mathematics; stochastic jumps; numerical methods for option pricing; continuous time models; derivative pricing models
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\textit{B. Hambly} et al., Quant. Finance 9, No. 8, 937--949 (2009; Zbl 1182.91176)

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