Derivatives

CHAPTER 46 VaR: Alternative Measures

Aims

• To examine non-parametric methods of estimating VaR such as historical simulation and bootstrapping procedures.
• To demonstrate how Monte Carlo simulation (MCS) is used to estimate VaR for portfolios containing options.
• To analyse variants on the traditional VaR approach such as stress-testing and extreme value theory.

46.1 HISTORICAL SIMULATION

When using the variance-covariance method to calculate portfolio-VaR, we assume returns are normally distributed – hence we can use the ‘1.65’ scaling factor in our VaR calculations (for the 5th percentile). But if returns are actually non-normal using ‘1.65’ is no longer valid and it would produce biased forecasts of VaR. Historical simulation (HS), directly uses actual historical data on returns to calculate VaR and does not assume a particular distribution for returns – we take whatever distribution is implicit in the historical data.

When we use the variance-covariance approach to measure risk we explicitly measure the variance (standard deviation) and the covariances (correlations) between each of the asset returns in our portfolio. These variance and covariances (correlations) are ‘parameters’. However, in the HS approach, variances and covariances are not explicitly estimated – hence the term ‘non-parametric’. Instead these features of the data are ‘encapsulated’ in the time path of actual returns used in the HS approach.

The HS approach is straightforward and intuitive. Consider Figure ...