Integrated Market and Credit Portfolio Models (eBook)

PD Dr. Peter Grundke habilitierte am Seminar für Allgemeine Betriebswirtschaftslehre und Bankbetriebslehre der Universität zu Köln. Er leitet zur Zeit das Fachgebiet Finance an der Universität Osnabrück.

Preface 6
Acknowledgments 8
Contents 9
List of Tables 12
List of Figures 14
List of Acronyms 15
List of Symbols 16
Chapter 1 Introduction 22
Motivation 22
Structure 25
Chapter 2 The Integrated Market and Credit Portfolio Model 27
General Approach 27
Industry Standards as Special Cases 29
Example of an Integrated Market and Credit Portfolio Model 31
Chapter 3 Effects of Integrating Market Risk into Credit Portfolio Models 39
Introduction 39
Review of the Literature 40
Modifications of the Base Case Model 45
Numerical Results 58
Conclusions 80
Chapter 4 On the Applicability of Fourier-Based Methods to Integrated Market and Credit Portfolio Models 82
Introduction 82
Review of the Literature 85
General Computation Approach 87
Numerical Results 90
Discussion 104
Importance Sampling Techniques for the Fourier-Based Approach 109
Conclusions 116
Chapter 5 Importance Sampling for Integrated Market and Credit Portfolio Models 118
Introduction 118
Review of the Literature 120
Importance Sampling Techniques for the General Approach 123
Numerical Results 154
Conclusions 173
Chapter 6 Conclusions 175
Appendices 178
Bibliography 183

Chapter 5 Importance Sampling for Integrated Market and Credit Portfolio Models (p. 99-100)

5.1 Introduction

As already mentioned in chapter 4, beside Fourier-based approaches, another efficiency enhancing computational approach developed for standard credit portfolio models is based on Monte Carlo simulations combined with variance reduction techniques. Most common is the application of importance sampling (IS) techniques.

In this chapter, it is shown in detail how a two-step-IS technique presented by Glasserman and Li (2005) for a pure default mode model can be applied to the general integrated market and credit portfolio model of section 2.1, and what differences exist. Glasserman and Li (2005) employ IS for the probability distribution of the systematic risk factors as well as for the conditional default probabilities to make higher losses more probable under the IS distribution.

In contrast, almost all other papers which deal with IS for credit portfolio models only apply one-step-IS techniques.56 That is why the technique suggested by Glasserman and Li (2005) is expected to be especially effective and why it is employed in this chapter. Furthermore, it is discussed how an IS approach originally developed by Glasserman, Heidelberger and Shahabuddin (2000) for pure market risk portfolio models can be combined with the two-step-IS approach to build up a potentially even more effective three-step-IS technique.

Glasserman, Heidelberger and Shahabuddin (2000) use a delta-gamma approximation of the loss variable of a portfolio of default risk-free instruments for selecting an effective IS distribution for the normally distributed vector of market risk factors. As we deal with integrated market and credit portfolio models, the idea to combine methods originally developed for pure market risk portfolio models with those originally developed for pure (default mode) credit portfolio models might suggest itself. However, up to now this has not been tried.

Summarizing, the main questions answered in this chapter are:

1) Are IS techniques originally developed for pure default mode credit portfolio models also applicable to integrated market and credit portfolio models?
2) How effective are they for these extended models?
3) Is it possible to increase the effectiveness by combining IS techniques originally developed for pure default mode credit portfolio models with those originally developed for pure market risk portfolio models ?

Chapter 5 is structured as follows. In section 5.2, related literature is reviewed. In section 5.3, after a short introduction into the IS technique, two- and three-step-IS techniques when applied to the general integrated market and credit portfolio model are presented. The particularities resulting from the integrated market risk are discussed. The effectiveness of the presented IS techniques is tested by means of numerical experiments in section 5.4. Finally, the conclusions and main results are summarized in section 5.5.