Modelling spikes and pricing swing options in electricity markets

Abstract

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.

Keywords:

• Energy derivatives
• Financial mathematics
• Stochastic jumps
• Numerical methods for option pricing
• Continuous time models
• Derivative pricing models

Notes

†They describe the method in terms of a complex valued characteristic function and Fourier inversion, but by allowing complex values the method can also be written in terms of Laplace transforms.

†This will also involve a ‘refraction period’ in which no further right can be exercised.

‡We could assume any general payoff function.

†This is actually an American option.

‡The rights of a swing option can only be exercised one at a time.