ArrowHead Models – Comprehensive Fundamental Models That Represent the Way Commodity Markets Work

ArrowHead Models Provide Accurate Representation of Future Markets with Intrinsic Probability Based on the Market Driver Assumptions

ArrowHead Models Significantly Differentiate Our Company and Services

Among the key aspects that differentiate our company and services are the ArrowHead Models. The models have been continuously improved over four decades and have been successfully used by our consultants and clients to help companies understand future markets and make the right decisions. Though accurately representing future market behavior is difficult and many other modeling methods have proven to be ineffective and unreliable, our clients have a high degree of confidence in ArrowHead model outputs for a variety of reasons.

Why Is Modeling Future Commodity Markets Difficult?

There are many reasons modeling future markets accurately is difficult:

Markets have extensive and comprehensive structure (e.g. oil and gas wells, pipelines, storage, mines, transportation and transmission, power plants, and emissions). Models must correctly represent the full structure and the way all these elements interconnect.
Each component in the market seeks to maximize profit, so the components must be represented as independent agents in the model. Agent modules must consider the investment, operation, and retirement decisions they would make under various conditions they face and select the decision that would result in the most profitable outcomes.
Global markets are comprised of myriad, interconnected regional markets and flows (e.g., gas, oil, electricity and coal). The model must therefore accurately represent existing and prospective interconnection of regions.
There are many potential market drivers (events or changes in market structure that affect prices and volumes), so models must have the ability to vary market-driving assumptions. The models must allow many combinations of different assumptions regarding potential drivers.
The many different drivers and potential events have different probabilities. The model must enable easy application of probabilities to events, creating not just single price streams but probability distributions over price (and quantity) over the time horizon of the analysis (from 0 to 50 years).
Fundamental economic modeling requires the application of sound economic science and probability theory. This is non-trivial given the complexity and interconnectivity of the markets. Using “junk economics” or “junk probability” simply won’t produce reliable results.
To have confidence in the model results, decision makers must be able to easily see and understand the model methodology and be able to easily see and adjust the model structure, data, and assumptions. Transparency and customizability are absolute musts.
Confidentiality of client information is paramount. Secure and efficient technology that stays current with best in class security methods and techniques to keep your information secure is required. At the same time, modeling technology must exploit best in class multithread/parallel computing to provide timely response, fast turnaround, and reduced analysis costs.

How ArrowHead Models Uniquely Meet These Requirements

The ArrowHead models uniquely meet all of these modeling challenges. Each of the ArrowHead models (Natural Gas, Power, Oil, and Metals and Other Commodities) are built on the same ArrowHead analytic and technical architecture.

Agent Based Architecture Accurately Represents Agents and Market Structure for Each Commodity

Within the ArrowHead models, there are many different individual agent objects, each of which accurately represents the operational and competitive characteristics of each market agent:

The “chemistry and physics” of the technologies those agents can deploy
The full capital and operating cost structure of those technologies
The full thermodynamics (losses and efficiencies)
The investment, operation, and retirement behavior in which those agents are able to engage

Each of the ArrowHead models is a network configuration of agents in which the network itself represents the structure of the relevant market (e.g., producers connected to field processing connected to pipe connected to customers and so forth). Each ArrowHead agent contains many easily adjustable parameters that represent the investment, operation, and retirement characteristics for that agent and thereby how that agent affects and is affected by the market. The agent nodes, which collectively in network form characterize market structure, individually represent not only the chemistry, physics, thermodynamics, and costs for that agent but also the profit seeking behavior of that agent, i.e., the incentives facing that agent. (Profit seeking is represented using sophisticated, correct mathematical principles.) Such a model represents how the markets will play out over the time horizon (from 0 to 50 years) based on agent by agent assumptions about costs, resources and demands, all of which are easily adjusted to characterize different combinations of potential future events. The architecture enables us to build up the multiregional global nature of gas and oil, the myriad interconnections among regions in power, the interrelationship of gas and power, and the like. The efficiency of the approach allows us our models to comprehensively represent the markets’ detail and scope.

ArrowHead Model Outputs

Model outputs are threefold: (1) prices, (2) flowing quantities, and (3) capacity additions (including retirements) for every commodity in every regional market in the model. For example, the power model is a detailed, interconnected model that calculates prices, quantities, and capacity addition/retirement streams over time for power, emissions, natural gas, coal, emissions credits, etc. at every market location at every point in time over the time horizon of the model. This contrasts with many other commercial models (as well as models used by other consultants) in which prices and quantities are merely inputs and which do not represent capacity addition at all. For example, other power models require input of emissions prices and quantities and input of installed capacities in place rather than computing them endogenously the way the ArrowHead models do. With such models, one has to assume what the prices and quantities would be, i.e., to assume the answers! To be helpful for decision making, economic models must compute, using economic first principles, forward price schedules, volume schedules, and capacity addition/retirement schedules endogenously over time. Lacking that, they cannot be accurate or reliable.

Probability Distribution over Price and Quantity

Easy adjustment of assumptions about market drivers enables many scenarios and delivers accurate understanding how markets will react under different combinations of potential events. Every potential event has a probability of occurrence, and ArrowHead uniquely allows probabilities to be applied by each individual agent to every potential 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. These are the inputs for pro formas to calculate profitability and value for assets and contracts. What could be more valuable to decision makers?

Incorporating probabilities correctly is non-trivial. ArrowHead knows how to correctly perform these calculations (using the Arrow State Contingent Pricing technique pioneered by the Nobel Laureate Kenneth Arrow, who is ArrowHead’s namesake). ArrowHead not only knows how to create probability distributions over individual prices, but also joint probability distributions over collections of prices. This means that our basis differentials are inherently probabilistic and contain all dependencies and correlations.

Transparency and Flexibility

The flexibility of the ArrowHead models, the ease with which market structure, operational characteristics of the components and assumptions can easily be changed, is a key ArrowHead distinction. The ArrowHead models are uniquely transparent, enabling clients to clearly see and understand the model components all well as methodology.

With every assignment, clients may choose to review as much of the model as they desire and specify changes they might prefer in the ArrowHead base case or any scenario. As that occurs, ArrowHead maintains highly secure, client-confidential, fully segregated versions of client models. This enables ArrowHead to perform client-specific analysis with a fast turnaround whenever important issues arise or speedy action or decisions are required.

ArrowHead Model Technology Meets Security and Other Key Needs

There is a key dimension of ArrowHead models and service that is crucial to clients, although not always directly visible. Security is a top priority for clients (and us). Our consultants guard clients’ information with their professional reputations and the reputation of our company. To assist, we use security technology that provides “best in class” level of security, and we upgrade as better technology emerges. Clients can be confident that their identity, their data, and their results are guarded by ArrowHead and the technology we use.

The architecture of ArrowHead models allows a solution method that is intrinsically parallel. Parallelization means that if you put twice the number of processors to work solving the model, you get the solution in half the time (approximately). The execution time scales approximately linearly with the number of processors you put into service. This means that parallel and cloud type computing give huge scalability and execution benefits. Scalability enables us to improve model run times by merely adding additional processors. Rather than long overnight (and often longer) runs, the ArrowHead models can produce results more quickly. This is helpful when rapid turnaround is needed and when there are very detailed probability distributions.

The network structure and agent data are key components of the architecture. The architecture enables easy, Excel-based access to and modification of both network structure and data. Excel facilitates easy data and scenario loading of entire models as well as parts of models when specific scenarios are desired or clients want to have us use their own data. Excel uploading reduces clients’ costs and facilitates fast turnaround. ArrowHead models have a sophisticated output reporting capability that downloads into Excel. This facilitates standardization, easy client use, and cross scenario comparison.