From calendar time to business time: the case of commodity markets

We address the problem of modeling commodity forward curves, while preserving empirical features observed in commodity markets. By letting a commodity market to "live"in the tempo of a business rather than calendar clock, we create a model with a rich but realistic set of features, such as stochastic volatility, stochastic rate of mean reversion and various shapes of forward curves such as backwardation and contango. The model, when applied to extensive historical datasets of crude oil and natural gas forward curves, shows a remarkably good fit to the observed futures prices, also in periods of high volatility and negative prices. The model is developed in such a way that it can be used for a wide variety of applications, ranging from exotic derivatives pricing to risk management of commodity portfolios.