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.
