# 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 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:

• fundamental model which is a system of postulates and data, together with a means of drawing dynamical inferences from them;
• 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;
• statistical model is a regression or best-fit between different data features.

In regulatory frameworks such as SR 11-7, the term “model” refers to a quantitative method, system, or approach that uses statistical, economic, financial, or mathematical theories, techniques, and assumptions to process input data into quantitative estimates. This is formed by three components: the information input component, the processing component and the reporting component.

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.

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