Analytical Approximation for the Price Dynamics of Spark Spread Options

This paper presents an analytic approximation for the pricing dynamics of spark spread options in terms of Fourier transforms. We propose to model the spark spread, that is, the price difference of electricity and gas, directly using a mean-reverting model with diffusion and jumps. The model is analyzed empirically, and shown to fit observed data in the UK reasonably well. The main advantage with the model is that the spark spread of electricity and gas forwards, being forwards with delivery over periods, can be priced analytically. The price dynamics for different spark spread options with electricity and gas forwards as underlying, is analytically derived through Fourier transforms. These pricing expressions allow for efficient numerical valuations via the fast Fourier transform technique.