Risk valuation for weather derivatives related to the energy market

Overview & Synopsis

With the increasing demand for climate risk transfer financial tools, climate derivatives have gained considerable popularity among both researchers and practitioners. This thesis contributes to deepening the understanding of the risk related to temperature and energy based derivatives. In Chapter 1, we develop a new stochastic volatility model for the average daily temperature that is a natural extension of the Ornstein-Uhlenbeck model proposed by Benth and Benth [16]. This model allows to be more conservative regarding extreme events while keeping tractability. We give a method based on Conditional Least Squares to estimate the parameters on daily data and estimate our model on eight major European cities. We then show how to calculate efficiently the average payoff of weather derivatives both by Monte-Carlo and Fourier transform techniques. This new model allows to better assess the risk related to temperature volatility. In Chapter 2, we focus on quanto derivatives. We develop a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products are quickly spreading as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and average daily temperatures are modelled through non homogeneous Ornstein-Uhlenbeck processes driven by a Brownian motion and a Normal Inverse Gaussian Lévy process, which allows to include dependency between them. A Conditional Least Square method is developed to estimate the different parameters of the model and used on real data. Then, explicit and semi-explicit formulas are obtained for derivatives including quanto options and compared with Monte Carlo simulations. Last, we develop explicit formulas to hedge statically single and double sided quanto options by a portfolio of electricity options and temperature options (CDD or HDD). All in all, this study contributes to the establishment of a mathematical framework to better understand risk related to temperature and energy derivatives while answering to both business and research challenges.