Analytic Models

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

See Also

• Simulation Models
• Semi-Analytic Models