Narrow Results

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.

An equivalent amount of metallurgical slag, water-quenched slag powder and activator was substituted for a part of the cement to prepare concretes at strength grades of C25, C30 and C40. Due to the filling effect, pozzolanic effect, micro-aggregate effect, and improvement of pore structure, the prepared concretes not only had greater strength compared with reference concrete, but also had greater impermeability and frostresistance. Moreover, the expansion reactions between alkali and aggregates were effectively inhibited. The slag and activator can serve as the raw materials for green concretes.