Three Methodologies for Calculating VaR

There are three major methodologies for calculating VaR.

  • Parametric
  • Monte Carlo
  • Historical

Note that the risk of nonlinear instruments (for example, options) is more complex to estimate than the risk of linear instruments (for example, traditional stocks, bonds, swaps, forwards, and futures), which can be approximated with simple formulas.

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:

TypeDescriptionUse
ParametricEstimates 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 CarloEstimates VaR by simulating random scenarios and revaluing instruments in the portfolioAppropriate for all types of instruments, linear or nonlinear
HistoricalEstimates 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

TypeAdvantagesDisadvantages
ParametricFast and simple to calculateLess 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.