Modelling and Numerical Valuation of Power Derivatives in Energy Markets

In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process. We focus on the derivation of the partial integro-differential equation (PIDE) which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation. For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part. Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven. Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters. In particular the effects of number of exercise rights, jump intensities and dividend yields will be investigated in depth.

Option Derivatives in Electricity Hedging

Despite the high volatility of electricity prices, there is still little demand for electricity power options, and the liquidity on the power exchanges of these power derivatives is quite low. One of the reasons is the uncertainty about how to evaluate these electricity options and about finding the right fair value of this product. Hedging of electricity is associated mainly with products such as futures and forwards. However, due to new trends in electricity trading and hedging, it is also useful to think more about options and the principles for working with them in hedging various portfolio positions and counterparties. We can quite often encounter a situation when we need to have a perfect hedge for our customer’s (end user consuming electricity) portfolio, or we have to evaluate the volumetric risk (inability of a customer to predict consumption, which is very similar to selling options. Now comes the moment to compare the effects of using options or futures to hedge these open positions. From a practical viewpoint, the Black-Scholes prices appear to be the best available and the simplest method for evaluating option premiums, but there are some limitations that we have to consider.