GHICA --- Risk analysis with GH distributions and independent components
- Chen, Ying
- Härdle, Wolfgang
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62G05 62H12 62H10
- independent component analysis, generalized hyperbolic distribution, adaptive volatility, Value-at-Risk
Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A principle component based method (tied closely to the elliptical structure of the distribution) is therefore expected to be unsatisfactory. Here we propose and analyze a technology that is based on 1) performing an Independent Component (IC) search and 2) adaptively fitting the resulting independent marginals by Generalized Hyperbolic (GH) distributions. We study the proposed GHICA methodology in an extensive simulation study. We then apply GHICA to exchange rate portfolios with different trading strategies and a high-dimensional German stocks portfolio. Our analysis with GHICA yields very accurate VaRs.