A model is a set of assumptions that describes a system using mathematical language. A model typically captures relationships amongst data.
As highlighted by Emanuel Derman, models 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 that 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. A model 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. that 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.