Operational Risk toward Basel III: Best Practices and Issues in Modeling, Management, and Regulation

CHAPTER 8

Importance Sampling Techniques for Large Quantile Estimation in the Advanced Measurement Approach

Marco Bee and Giuseppe Espa

 

 

ABSTRACT

In most cases, in the advanced measurement approach, the loss distribution cannot be obtained in closed form, so that probabilities of losses exceeding a given monetary amount have to be computed by means of simulation techniques. If this probability is small, importance sampling is the most efficient method. In this chapter we show how to choose optimally the importance sampling density in the compound Poisson setup under different hypotheses for the severity distribution.

8.1 INTRODUCTION

The measurement and management of operational risk have experienced a rapid growth in the last few years. The main reason probably has been increased regulatory pressure, witnessed by the explicit introduction of this type of risk in the New Basel Capital Accord (Basel 2005). The most sophisticated approach listed by the Basel II Accord is the so-called Advanced Measurement Approach (AMA), which is typically adopted by the largest banks. Roughly speaking, it allows banks to build their own internal models, similar to what happens for the measurement of market and credit risk. From the methodological point of view, however, operational risk is based on different techniques, mainly because losses are not related to financial grounds.

The actuarial methodology, with particular reference to the techniques of the non-life insurance field, plays ...