Klaus Böcker

Multivariate models for operational risk

Böcker and Klüppelberg [Risk Mag., 2005, December, 90–93] presented a simple approximation of OpVaR of a single operational risk cell. The present paper derives approximations of similar quality and simplicity for the multivariate problem. Our approach is based on the modelling of the dependence structure of different cells via the new concept of a Lévy copula.

Modeling and measuring multivariate operational risk with Lévy copulas

Simultaneous modelling of operational risks occurring in different event type/business line cells poses a serious challenge for operational risk quantification. Here we invoke the new concept of Levy copulas to model the dependence structure of operational loss events. We explain the consequences of this dependence concept for frequencies and severities of operational risk in detail. For important examples of the Levy copula and heavy-tailed GPD tail severities we derive first order approximations for multivariate operational VAR.

Interaction of market and credit risk: an analysis of inter-risk correlation and risk aggregation

In this paper we investigate the interaction between a credit portfolio and another risk type, which can be thought of as market risk. Combining Merton-like factor models for credit risk with linear factor models for market risk, we analytically calculate their interrisk correlation and show how inter-risk correlation bounds can be derived. Moreover, we elaborate how our model naturally leads to a Gaussian copula approach for describing dependence between both risk types. In particular, we suggest estimators for the correlation parameter of the Gaussian copula that can be used for general credit portfolios. Finally, we use our findings to calculate aggregated risk capital of a sample portfolio both by numerical and analytical techniques.

Economic Capital Modelling and Basel II Compliance in the Banking Industry

Risk is an inevitable part of every financial institution, above all banks and insurance companies. Risks are implicitly accepted when such institutions provide their financial services to customers and explicitly when they take risk positions that offer profitable, above-average returns. There is no unique view on risk and usually it is considered in certain sub-classes such as market risk, credit risk and operational risk, also interest rate risk and liquidity risk. Market risk is associated with trading activities; it is defined as the potential loss arising from adverse price changes of a bank’s positions in financial markets and encompasses interest rate, foreign exchange, equity and creditspread risk. Credit risk is defined as potential losses arising from a customer’s default or loss of credit rating. Such risks usually include loan default risk, counterparty risk, issuer risk and country risk. Finally, operational risk is due to losses resulting from inadequate or failed internal processes, human errors, technological breakdowns, or from external events.