What is a Model?
A model is a set of assumptions that describes a system using mathematical language.
It typically captures relationships amongst data.
As highlighted by Emanuel Derman, these come in various types. The three most important categories are:
- A fundamental model which is a system of postulates and data, together with a means of drawing dynamical inferences from them;
- A phenomenological model, i.e. a description or analogy that does not attempt to understand the underlying dynamics of a system but can be useful e.g. in the context of visualization;
- A statistical model is a regression or best-fit between different data features.
In regulatory frameworks such as SR 26-2, the term “model” refers to a complex quantitative method, system, or approach that applies statistical, economic, or financial theories to process input data into quantitative estimates. The term “model” in this guidance excludes simple arithmetic calculations, such as those found within spreadsheets, as well as deterministic rulebased processes and software where there are no statistical, economic, or financial theoriesunderpinning their design or use.
To be classified as a model under this guidance, a system must generally possess three distinct functional parts:
- Information Input: This component delivers data and assumptions (e.g., market prices, historical loss data, or expert judgment) into the system.
- Processing: This is the "engine" that transforms those inputs into estimates using mathematical or statistical logic (e.g., a regression analysis, a Black-Scholes formula, or a machine learning algorithm).
- Reporting: This component translates the raw estimates into actionable business information (e.g., a credit score, a Value-at-Risk number, or a projected loss).
The difference between a model and an algorithm is that a model is a set of assumptions while an algorithm is a recipe to solve the equations linked to a particular model. As one example, the Hull-White model can be used to describe the dynamics of the interest rate curve. The underlying assumptions are a.o. the short rate is driven by a mean-reverting stochastic process. To compute the NPV of a derivative as given by the Hull-White model, we can use a Monte-Carlo algorithm to perform the numerical integration.
Examples of a Model
- Online Retail Recommendation Engine
- Purpose: To predict the likelihood (a quantitative estimate) that a specific customer will purchase a product.
- Fit to Definition: It applies statistical and machine learning theories (like collaborative filtering) to process input data (past purchases, browsing history) into a final quantitative estimate (a ranked purchase probability score) for reporting.
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- A City's Traffic Flow Optimization System
- Purpose: To predict traffic volume at a particular intersection and adjust traffic light timing to minimize congestion.
- Fit to Definition: It applies mathematical and statistical techniques (like time-series forecasting and queuing theory) to process input data (real-time sensor data, historical congestion patterns) to produce a quantitative estimate (a predicted wait time or optimal light cycle length).
Example of What is NOT a Model
A Basic Sales Tax Calculator in a Spreadsheet
- Purpose: A basic spreadsheet or calculator function that takes an item price and multiplies it by a fixed, legislated sales tax rate to determine the final cost (e.g., Price * 1.07). This is a simple, deterministic rule—it involves no complex statistical theory or subjective assumptions, thus falling into the category of a simple quantitative tool, not a model.
- Reason for Exclusion: The text specifies that a "quantitative tool" that uses deterministic rules rather than theories or assumptions is generally excluded.
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