Theoretical and Computational Analysis and Comparison of Stochastic Models of Energy and Interest Rate Markets

Abstract

The present work summarizes information about Interest Rate Market and Energy Market. A mathematical framework is the main aspect considered here. Different kinds of stochastic models are described for both markets. In addition, an introduction is given to a very interesting approach developed by Hinz et al. in 2005. The idea is in an application of interest rate market techniques to the energy market. Comparing this approach to the standard stochastic model we obtain the connection between two different sets of parameters. This significantly extends the possibilities of estimating the crucial parameters of the model. In the final chapter we explore two different ways of using Heath-Jarrow-Morton framework. Firstly, we estimate parameters of the model using a specific form of volatility function and sweet crude oil forward prices. Finally, we examine the general form of volatility function of natural gas forward prices. Then using Principal Component Analysis we obtain the main principal components which allow us to reproduce prices of forward contracts.