Energy Prices – Crude Oil
It is known that energy prices are somewhat different than other prices set in financial markets. Due to short term supply and demand imbalance prices of energy could float dramatically. Also news from politics, interest rate markets or shipping markets could also bring an uncertain factor to energy market. There are several important properties associated with volatility of spot energy prices, including: seasonality, mean reversion, and price spikes. For these reasons pricing, measuring, and managing the risk of energy contracts become an extremely complex task.
As a student of financial engineering in this article I would like to use financial modeling tool to help energy market participant make rational decision in trading or hedging. This article includes three parts of work. At first Principle Component Analysis will be applied to model the dynamics of the evolution of the crude oil (WTI) forward curve. Value-at-Risk is calculated the end of the part. After that to model the crude oil price I built a NGARCH process to fit the model. In the third part Ornstein-Uhlenbeck process is introduced to model the natural gas price. Value-at-Risk indicated by the two models will be calculated following the models.
Part One Forward Curve Analysis
A model of the evolution of the forward curve is crucial in any energy trading and risk management practice. With a good model of forward curve we can have a better estimation of earning, P/L, or Value-at-Risk.
Forward curves are a collection of forward prices for different maturities. The forward price curve can take a whole variety of shapes depending on the market and the time period analyzed. Some methodologies used to capture the evolution of forward curve require information about the volatilities and correlation of the whole matrix. As the increase of dimensions of the matrix, the complexity of this type of approach increases sharply. With so many parameters to estimate, the calculation is difficult.
Here we will use a nonparametric method Principal Component Analysis (PCA) to analyze the forward curve. Using PCA, we can reduce the number of dimensions of problem.
Future Data Analysis
I use the futures data on crude oil between. Figure 1 is the summary of futures price of crude oil in this period.
Figure 1
The correlation matrix of the different maturities futures is show in Figure 2. The single point (x, y, z) in the diagram denotes the covariance between future with maturity x and future with maturity y. The high correlation among the futures contracts means that only a few principle components are necessary to explain the variation of the forward curve.