Page 160 - Contributed Paper Session (CPS) - Volume 7

CPS2051 Mentje G. et al.

Construction of forward looking distributions
using limited historical data and scenario
assessments
Mentje Gericke, Helgard Raubenheimer, PJ (Riaan) de Jongh
Centre for Business Mathematics and Informatics (BMI), North-West University

Abstract
Financial institutions are concerned about various forms of risk. The
management of these institutions have to demonstrate to shareholders and
regulators that they manage these risks in a pro-active way. Often the main
risks are caused by losses that occur due to defaults on loan payments or by
operations failing. In an attempt to quantify these risks, the estimation of
extreme quantiles of loss distributions is of interest. Since financial companies
have limited historical data available and need to provide a forward-looking
view, they often use scenario assessments by experts to augment their
historical data. This paper gives an exposition of a particular statistical
approach that may be used to combine historical data and scenario
assessments in order to estimate extreme quantiles.

Keywords
Loss distribution approach; scenario information; operational risk; economic
capital; quantile estimation

1. Introduction
All financial losses need to be carefully managed and provided for by
financial institutions. For example, banks are required by regulatory authorities
to set aside capital to absorb unexpected losses. In addition, they also
calculate economic capital, being the amount that a bank estimates it may
need in order to remain solvent at a given confidence level and time horizon.
The focus of this paper will be on operational risk in banks.
Financial institutions are more interested in the aggregate loss that may
occur over one year in the future, than the individual losses in a particular area
or business line. Popular modelling methods involve the construction of
annual aggregate loss distributions using the so-called loss distribution
approach (LDA). The constructed distribution may be used to answer
questions like ‘What aggregate loss level will be exceeded once in c years?’ or
‘If we want to guard ourselves against a one in a thousand year aggregate loss,
how much capital should we hold next year?’ The aggregate loss distribution
and its quantiles provide answers to the above questions and therefore the
distribution should be modelled as accurately as possible. It is often the
extreme quantiles of this distribution that is of interest, for instance, the

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