טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentWilly Elizarov
SubjectA Principal Component Model for Commodity Futures
DepartmentDepartment of Industrial Engineering and Management
Supervisors Professor Reisman Haim
Mr. Zohar-Zalman Gady


Abstract


In this work we suggest a new approach for commodity futures prices modeling, which allows relaxing the no-arbitrage constraint. We first build a Factor Model, which can be considered as a generalization of the Schwartz model (1997). While the Factor Model is based on no-arbitrage argument, we are interested to find arbitrage opportunities in futures markets. With this end in view, we introduce a new Principal Component Model (PCM) for commodity futures by modeling price dynamics of commodity futures using Principal Component Analysis (PCA). Using our Factor Model’s structure, we implement the PCA to available market data, by Singular Value Decomposition method. It is important to note that, unlike other models, our approach does not impose the no-arbitrage constraint. As a result, the goodness of fit for our estimators is at least of the same quality. In the next step, we calculate a theoretical arbitrage rate using the estimated principal components. While solving a maximization problem for the arbitrage rate, we also define the optimal trading strategy for our setting. Then we test the obtained optimal strategy on real crude oil futures data from the London International Petroleum Exchange. We examined various portfolios, omitting the closest to maturity (and the most volatile in this portfolio) contract in each. In order to compare different portfolios, we measured our results in terms of the Sharpe Ratio. The empirical results are quite encouraging.