Author(s)

M. Di Pierro & A. Nandy

Abstract

In this paper we propose a Monte Carlo based approach to Risk Management. Our approach applies to any system subject to random uncorrelated losses under very general conditions. Our methodology consists of the following steps: model the distribution of losses and the distribution of time intervals between losses via an analysis of historical data; perform a Monte Carlo simulation of a finite period of time in the future; use the Monte Carlo data to estimate the 99.9% VaR. 1 Introduction In this paper we present an approach to Risk Management based on the Monte Carlo technique. The proposed approach is very general and it can be applied to any system characterized by discrete losses. We have made the following broad assumptions: a) loss events are independent; b) number of loss events occurring in any time interval ∆T is independent of loss events occursing before the time interval considered; c) the probability of two events occurring at exactly same time is zero. Discrete losses due to internal fraud (i.e. Operational Risk as defined by Basel II accord) for a particular department in a Bank provide a good example of application [1]. Our approach is based on the following steps: 1) model the time distribution and the severity distribution of losses; 2) simulate possible future scenarios compatible with the observed time and severity distributions; 3) compute the 99.9% VaR as the monetary amount that is greater than the total loss in 99.9% of the simulated scenarios. Notice that our approach is free from bias or assumptions about the distribution of the total loss. The validity of the assumptions a), b) and c) can be verified directly from the data, as we show in the example of section 3.

Keywords