# Analytic Models

From Open Risk Manual

## Definition

**Analytic Models** (also *Analytic Solutions*) are mathematical models that can be expressed in succinct notation using well known mathematical functions / formulas (Also **Closed Form Models** or simply **Formulas**). Several areas of risk management have developed analytic models to assist with Risk Measurement

## Usage

A list of advantages of an analytic model includes:

- immediate oversight of model content, the role of model parameters etc
- availability of powerful mathematical tools to analyse the model structure (e.g. perturbation theory)
- relatively easy implementation in widely available platforms (e.g. spreadsheets)
- fast execution (supported by the existence of optimized implementations of well known functions)

## Examples

- The Black-Scholes pricing formula
- The Mean-Variance Model for Portfolio returns
- The ASRF model of portfolio credit loss

## Issues and Challenges

- Realistic problems tend not be "analytically" tractable, which prompts alternative methods such as
**semi-analytic models**, Simulation Models or Economic Scenario Generator based approaches - Analytic approaches may potentially sacrifice significant features (fidelity) in the pursuit of tractability