# MODELLING ELECTRICITY PRICES AND PRICING DERIVATIVES WITH MARKOV REGIME SWITCHING MODELS

• Rashed Alghanim

Student thesis: Phd

### Abstract

In liberalised electricity markets, spot prices exhibit distinctive features, such as mean reversion and spikes, that are more pronounced in electricity compared to other commodity markets. Markov regime-switching models are considered efficient candidates for capturing the main characteristics of electricity price dynamics. We propose four models of Markov regime-switching that describe the spot prices themselves rather than log prices with different specifications for base and spike regimes. In particular, the base regime in the first and second models follow the geometric Brownian motion process while the spike regime in these models follow normal and log-normal distribution, respectively. In the third and fourth models, the dynamics in the base regime follow the Ornstein Uhlenbeck process while the dynamics in the spike regime for the two models are described by the Brownian motion with drift and mean reverting pure jump process, respectively. For each model, we discuss its advantages and statistical properties for describing the spot price dynamics and pricing derivatives. We also perform simulations for the path of the proposed models. The pricing of the derivatives on such models is based on the splitting up of a derivative price in a mean-reverting component and a spike component due to the independent feature of regimes in the Markov regime-switching model. We derive analytical pricing formulas for forwards under the proposed models. We then obtain the dynamics of the forward curve implied by the spot price model. We also consider the pricing of European call and barrier options. We obtain closed-form formulas for the price of call option under models 1, 2 and 3. For model 4, the call option price is calculated using the Fourier transform. Based on the joint density of Brownian motion and its maximum, we have the explicit pricing formula for barrier option under model 2, where the spike regime follows the Brownian motion. Also, a partial differential equation approach is employed to price barrier option under model 3.
Date of Award 1 Aug 2019 English The University of Manchester Tusheng Zhang (Supervisor) & Denis Denisov (Supervisor)

### Keywords

• energy market
• regime switching model
• derivatives pricing
• Electricity price modelling

'