This study suggests algorithmic procedures for calculation of value-at-risk and conditional-value-at-risk using Pearson's family of distributions. This family contains most of classical distributions, including heavy tailed ones, like t-distribution, etc. It has been noticed that the best fitting t-distributions for financial data often assume non-integer degrees of freedom. Calculation of risk measures in this case can be simplified by incorporating a simple analytical relation between degrees of freedom and kurtosis, suggesting a correction term in calculation of VaR. We extend these findings on Pearson class of distributions. Suggested procedures are streamlined for risk management applications, and, using Mathematica package,- presented in analytical form, wherever possible. Numerical work has been carried out by S-Plus and Mathematica computing packages. Examples of calculations for several financial time series are also included.
|Effective start/end date||09.01.2003 → 01.01.2008|