Risk capital stress-testing framework and the new capital adequacy rules

Håkan Andersson, Andreas Lindell

Abstract

ABSTRACT

We propose a general framework for simulating the value of a financial portfolio over time. The main idea is to let experts specify the longterm behavior of the economy, and use statistical models to generate the behavior at intermediate time points. First, a set of expert scenarios specifying the values of the dominant risk factors at a few discrete time points is determined. Then, for each of these scenarios, a continuoustime model is specified that is consistent with the expert scenario. As a working example we simulate the equity of a model bank mainly involved in retail business activities, such as lending to households and small corporates, deposit services, brokerage and different types of payment services. We specify a continuous-time model for the bank's daily revenues and costs given expert scenarios specifying the long-term development of the macroeconomy, client volumes, margins and fees. The ruin probability, ie, the probability that the equity ever becomes negative, is investigated in some depth. Inspired by the work of Jokivuolle and Peura (2004), we also show how the new capital adequacy rules (Basel II) can be included in our framework. The Basel accord specifies calculation rules for the eligible capital as well as for the amount of risk (referred to as "Risk Weighted Assets") that the bank is exposed to. We perform a joint simulation of the capital and the risk weighted assets in order to investigate if the regulatory requirements are fulfilled in all the scenarios.