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