Keywords: energy based assets, spot prices, futures prices, option on spot, futures options, delta hedging, transaction costs, perturbation analysis, climate change, carbon financing, sustainability, modelling, supply-demand imbalances, option prices, Monte Carlo simulation
Energy-based assets: modelling, option pricing and delta hedging with transaction costs
The growing significance of climate change and carbon financing means it is becoming increasingly important to generically model energy-based assets in a more theoretically consistent and realistic approach. A fundamental feature is supply-demand imbalances and this is modelled by deterministic sinusoidal functions on multiple time scales. This is unrealistic and theoretically inconsistent with scientific and financial models. We propose a new generic model for energy-based assets using Ornstein?Uhlenbeck processes on multiple time scales, which captures supply-demand imbalances in a more theoretically consistent and realistic manner. We analyse its properties and derive closed form solutions to European option prices on the underlying spot and futures processes. We derive a closed form analytic equation for delta hedging options under transaction costs using a perturbation analysis. We conduct numerical experiments on our model by calibrating it to Nord Pool electricity data and executing Monte Carlo simulation over 10,000 sample paths.