Abstract

Operational risk modelling is one of the most challenging risk types due to its serious impact on the health of financial institutions as well as lack of data leading to modelling difficulties. It follows that it is quite hard to get reliable estimate of the probability distribution of risk events, as concerns both, the frequencies and the severity, and simultaneously, there is a need to estimate the risk levels in the tails. In this paper we focus on the case of one financial institution with rather insufficient databases of risk events and try to estimate the risk (in terms of VaR and cVaR) using various kinds of Lévy models. The results show that there can be quite significant differences among weekly- and monthly-aggregated data especially in the tails, though rather simplifying Gaussian distribution does not strongly differ from theoretically more appropriate gamma or Weibull distributions.

INTRODUCTION

The business of financial institutions is based on confidence of potential clients in their financial healthiness and creditworthiness and long-term existence. Since distress of one financial institution can be easily transmitted to another entities and even to the whole sector and thus harm whole economic environment in the country, one of the crucial points of economic policy is to create efficient and reliable system of regulation and supervision of financial institutions. Since governmental policy is commonly related to a political cycle, in most countries the supervision process is independent on it. However, setting of the regulation rules often remains in the discretion of government. In this analysis we focus on operational risk data collected in one financial institution and consider several probability distributions, with special focus on Lévy models, and their dependency functions to see the impact on overall risk measure. We proceed as follows. In Section 2 we review theoretical foundations of operational risk modelling and some previous results on their implementation. Next, in Section 3 we define the models which we consider in this ana ...