ArrowHead Models – Metals and Other Commodities

ArrowHead Global Metals and Other Commodities Models Represent the Way These Global Commodity Markets Work throughout the World

Models for Many Other Commodities Have All the Unique Functionality and Benefits of the ArrowHead Energy Models

ArrowHead and its antecedent companies have modeled a number of non-energy commodities for clients over the years, including:

  • Copper
  • Aluminum
  • Iron and steel
  • Ammonia and urea
  • Phosphate
  • Timber
  • Agricultural products
  • Semiconductor chips
  • Lithium
  • Rare earths

These and other commodities (Metals and Other Commodities) are modeled quickly using the same ArrowHead modeling infrastructure used for the energy models. Creation of these commodity models is quick, reliable, and accurate:

  • Network (supply chain) structure and market element data, key requirements for model development, are readily available for most commodities. ArrowHead and its partners have market specialists who are knowledgeable of specific network (supply chain) structure and location of the key data for commodity industries.
  • The ArrowHead architecture enables easy loading of this network structure and data from Excel files.
  • The ArrowHead architecture contains many objects for representing many diverse market agents. Each object has considerable flexibility, enabling it to accommodate the unique agent structure, operational and competitive characteristics of the technology the agent uses, and agent behavior (i.e., pursuit of profit).
  • All of the other key aspects of ArrowHead Models are represented in these commodity models:
    • Accurate Market Representation. The flexible objects enable representing unique characteristic of each market, such as global connectivity or market contracts.
    • Outputs. Model outputs: (1) Prices, (2) flowing quantities, and (3) capacity additions (including retirements) for every commodity in every regional market in the model at every point in time across the time horizon (0 to 50 years).
    • Probability Distribution over Price and Quantity. ArrowHead uniquely allows probabilities to be applied by each individual agent to every potential market event. The model intrinsically incorporates event probabilities in the calculation of future market prices and quantities, producing not just a single price and quantity for each point in the market for each point in time but in fact a full probability distribution over price, quantity, and capacity additions.
    • Transparency and flexibility. Using the many flexible parameters in the models, easy adjustment of assumptions about market drivers enables many scenarios to be analyzed and delivers accurate understanding of how markets will react under different combinations of potential events.
    • Security and Scalability. State-of-the-art security protects the confidentiality of client information. The scalability of the architecture enables quick turn-around for model runs providing more productive analysis.

Examples of the ArrowHead Metals and Other Commodity Models

Iron and Steel

ArrowHead modeling is uniquely suited for the modeling of the iron and steel global commodity market. Figure 1 shows the output of a mining and milling region. Typically a region will produce pellets (concentrated iron ore). However, it can also produce directly reduced iron, and these two compete to meet the same demand. Pellets are transported to blast furnaces, which combine with coke to create pig iron. Directly reduced and scrap (recycle) iron are transported to mini mills (electric arc furnaces or EAF). There is potential intercourse between ladle steel (basic oxygen furnace or BFO output) and EAF feedstock. The output of the BOF and the EAF, final steel, is fabricated into such products as rod, bar, sheet, bloom, etc. Each of those products has a demand curve as shown. It is easy to see how ArrowHead represents iron and steel supply and demand chains in a particular region as shown in the figures below.

Figure 1: Single Regional Iron and Steel Manufacturing and Demand

Figure 1: Single Regional Iron and Steel Manufacturing and Demand

ArrowHead extends this to multiple regions in a continent or around the world by reproducing Figure 1 for each region and interconnecting them using bidirectional transportation links as in Figure 2. Attaching an upstream regional mining sector creates a world, integrated iron and steel model that predicts price, quantity, and capacity addition on a forward basis under uncertainty.


Figure 2: Multiregional Iron and Steel Manufacturing and Demand

Figure 2: Multiregional Iron and Steel Manufacturing and Demand


The upstream supply chain for lithium oxide is shown in Figure 3. Lithium rich salt deposits are solubilized at the lower right. Then there is selective solubility which concentrates the native LiCl in solution and separates the waste brine (e.g., NaCl). The concentrated LiCl solution goes into precipitation and drying, where a carbonate source (carbonic acid or even gaseous CO2 and water) is added to create Li2CO3 as a solid precipitate. Then the solid is calcined to replace the carbonate and create a solid oxide Li2O for use in subsequent refining to finished products. We can see the supply chains that comprise the lithium leaching process, and we can conceive how they connect into finished lithium metal, battery, and other finished products at the Li2O node in the figure. This complete model represents the network structure for the full global market structure and will accurately calculate the price forward in time, the quantity forward in time, and the capacity additions forward in time of all the elements in Figure 3.

Figure 3: Upstream Lithium Oxide Supply Chain

Figure 3: Upstream Lithium Oxide Supply Chain

ArrowHead Metals and Other Commodity Models Are Created with Ease like Loading an Excel Worksheet

Without the ArrowHead modeling infrastructure creating an accurate economic model for a global commodity is really a bridge too far. It is fraught with risk of never being completed. It would be extremely expensive, require a long time to develop, and would still lack many of the differentiating capabilities of the ArrowHead Models.

Using the ArrowHead Modeling Infrastructure, developing new models is similar to using Excel worksheets. Developing models in ArrowHead is like populating data in a worksheet. You don’t need to develop Excel for each new application, not even the worksheet, just load the data and test. The resulting model has all the functionality and accuracy of the ArrowHead Energy Models.

Commodity Models Uniquely Incorporate Uncertainty and Output Probability Distributions over Price and Quantity

Superimposed over the structural detail is the notion that all the agents operate under uncertainty. Probabilities are endogenous in commodity models, fully considered by agents in their investment, operation, and retirement decisions. Agent actions in the face of probabilistic “states of the world” hedge and avert risk. This determines price (or more formally probability distributions over price in every region of the world). Commodity models uniquely calculate probability distributions over prices and quantities in a full world supply-transport-demand context with endogenous agent-by-agent probabilities. There is no other commercially available model in the industry that provides a probabilistic, multiregional, multi-technology representation of world gas supply, transportation, and demand. Each ArrowHead commodity model’s output is a full probability density function over price and quantity, and also over basis, capacity additions and retirements.

Model Transparency and Adjustability Based on Client Need and Perspective

As with all of our models, the data and the structure are transparent and easily viewable by clients. For any analysis that we perform, the data, market structure, and all assumptions can be reviewed by clients. Adjustments can be made, whether to a client base case or to create specific scenarios. Transparency and customizability, combined with the time-tested methodology of our commodity models, are the reasons they have help clients clearly understand future markets and make correct, profitable decisions.