Handbook of Heavy Tailed Distributions in Finance

7 Stable modeling of portfolio risk for symmetric dependent credit returns

In this section we suppose that distributions of credit returns are symmetric α-stable and dependent. We interpret a symmetric random variable as a transformation of a normal random variable. Based on this interpretation, we develop a new methodology for correlation estimation. We apply the methodology for portfolio risk assessment.

We evaluate portfolio risk by determining portfolio VaR: (i) simulating a distribution of the $R_P={{\displaystyle \sum }}_{i=1}^n{w}_i{R}_i$ values; (ii) finding a certain quantile of the R_P distribution, say, the 1% quantile, which corresponds to the 99% VaR confidence level. ...