Risk Measures and Capital Allocation.

摘要

This research first gives a review of risk measures and risk capital allocation, along with the important property of coherency, and the relationships between different coherent risk measures. Secondly, relative accuracy measures are used as model-based criteria to study whether or not bias adjustment by various bootstrap techniques could improve estimates of the expected shortfall (ES) as a risk measure. Thirdly, different tests for backtesting Value-at-Risk (VaR) and ES are investigated as data-based criteria of evaluating risk models. Fourthly, multivariate framework is developed for estimating (conditional) ES and ES risk contributions (ESC), as a principle of capital allocation. Finally, an empirical study of estimating ES and ESC with backtesting is carried out for historical data from Russell Indices.