Volume 3 — Valuation and Risk Metrics © Copyright 2002, CCRO. All rights reserved. 11 More detail on each of these components is provided below in the Calculation section. There may be other assumptions that must be considered in the calculation, such as correlation and volatility, but they are not discussed in detail in this paper (extensive literature exists if more detail is needed). For comparative purposes across different business units (in the same company) or different companies, one must be careful to make sure the components of the VaR methodology are consistent. The differences in the parameters in the VaR metric listed above can lead to different measurements for risk in the case of an identical portfolio. This leads to considerable variation in the reported performance numbers and makes comparability across time and across companies that much more difficult. The same difficulty applies to interpretation of other risk and performance metrics (discussed in later sections of this white paper), compounded by differences in the way in which these metrics are derived. As a very important step in addressing this problem, the CCRO recommends that a common set of specified parameters be used for comparative analyses. A common methodology that can be applied to all contract, asset, and trading positions is most beneficial for creating transparency about risk. For guidance on the most appropriate way to report VaR to external stakeholders, see the Risk Management Disclosures White Paper. Regardless of the assumptions used for disclosure purposes, however, companies can use their own methodology and assumptions for internal business management. 3.2 Calculation Methodologies The three main methodologies for calculating VaR are: • Parametric, closed form, or variance/covariance • Monte Carlo • Historical. Parametric, Closed Form, or Variance/Covariance Analysis: This methodology estimates VaR using an equation that specifies parameters such as volatility, correlation, delta, and gamma. It is a fast and simple calculation, and extensive historical data are not required only volatility and a correlation matrix are needed. The methodology is accurate for linear instruments but less accurate for nonlinear portfolios or for skewed distributions. Monte Carlo Simulation: The Monte Carlo methodology estimates VaR by simulating random scenarios and revaluing positions in the portfolio. Extensive historical data are not needed. The method is accurate (if used with a complete pricing algorithm) for all instruments and provides a full distribution of potential portfolio values, not just a specific percentile. Monte Carlo simulation permits use of various distributional assumptions (normal, T-distribution, normal mixture, etc.). Thus, it can address the issue of fat tails, or leptokurtosis, but only if market scenarios are generated using appropriate distribution assumptions. A disadvantage of this