Modeling risk-weighted assets and the risk sensitivity of related capital requirements

Ernst Eberlein, Dilip Madan and Wim Schoutens

Abstract

ABSTRACT

The use of internal bank models for meeting capital requirements has been approved for some time. Regulators thus face issues of model approval, necessitating some public domain analysis of model performance. This paper presents a new approach to risk model evaluation using forward-looking risk-neutral probabilities. In addition to value-at-risk and conditional value-at-risk, we analyze a new measure, termed here risk-weighted asset value-at-risk (RWAVaR), that was proposed in a 2011 work by Carr et al. The new measure is a formalization of the popular concept of risk-weighted assets used in the Basel approach to capital requirements. The formalization allows for a possible leveraging of information contained in bid and ask prices and this paper reports on the potential of this approach. Capital measures using RWAVaR are observed to be sensitive to volatility, the volatility-of-volatility, the skewness of return distributions and the volatility spread across maturities. Movements in bid-ask spreads also strongly influence capital requirements. Additionally, there is the potential for some procyclicality to be built into the requirements, particularly when we adapt requirements to movements in liquidity spreads.