Financial instruments are nonlinear when their price does not change by a constant amount given a small movement in an underlying reference asset.
Brief Description
Brief description and use of each approach:
| Type | Description | Use |
|---|
| Parametric | Estimates VaR with equation that specifies parameters (for example, volatility and correlation) as input. | Accurate for traditional assets and linear derivatives, but less accurate for nonlinear derivatives |
| Monte Carlo | Estimates VaR by simulating random scenarios and revaluing instruments in the portfolio | Appropriate for all types of instruments, linear or nonlinear |
| Historical | Estimates VaR by reliving history; we take actual | |
| historical rates and revalue a portfolio for each | | |
change in the market | Appropriate for all types of instruments, linear or non-linear |
Advantages and Disadvantages
| Type | Advantages | Disadvantages |
|---|
| Parametric | Fast and simple to calculate | Less accurate for non-linear portfolios |
| Monte Carlo | - Accurate for non-linear instruments
- You get a full distribution of potential portfolios (not just a specific percentile)
- You can use various distributional assumptions (normal, T-distribution, and so on) | Takes a lot of computational power (and hence a longer time to estimate results) |
| Historical | - Accurate for non-linear instruments
- You get a full distribution of potential portfolios (not just a specific percentile)
- No need to make distributional assumptions | - You need a significant amount of daily rate history (at least a year, preferably much more)
- You need significant computational power for revaluing the portfolio under each scenario. |
From a user's perspective, the important point to remember is that if you have significant nonlinear exposures in your portfolio, a simulation approach will generally be more accurate for estimating VaR than a parametric approximation--however, at the cost of greater complexity and computational requirements.
Three Approaches
All three approaches for estimating VaR have something to offer and can be used together to get a more robust estimate of VaR. For example, a parametric approach may be used to get an instant snapshot of risks taken during a trading day, while a simulation approach may be used to provide a fuller picture of risks (in particular, nonlinear risks) on a next-day basis.
