This paper deals with the valuation of credit risk derivatives on the basis of Monte
Carlo simulation methods with the main viewpoint on variance reduction techniques.
Therefore, first an overview on credit risk derivatives like credit default swaps and first
to default baskets is given. It turns out that modelling of the joint distribution of
dependent credit default times proves to be the crucial element. Once obtained, any
credit derivative can be valued. A convenient way of achieving this is by use of the
copula concept, which migrates marginal distributions of credit default times obtained
from a credit curve into a joint distribution incorporating any kind of desired dependency
structure. A section devoted to this concept provides the necessary background
and properties. Next, the general Monte Carlo concept is introduced in detail and carefully
adapted to the valuation of credit derivatives, following the path of constructing
dependent uniform random variables from dependent normal random variables. At the
same time, first insight is gained in the field of variance reduction which is intensified
in chapter four, where a series of techniques including antithetic sampling and control
variates is presented. The main focus shall lie from there on on importance sampling.
In order to increase the efficiency of Monte Carlo methods, sampling is restricted to the
region of importance where the function to be evaluated - here: the indicator function
of the credit default times - does not vanish. This technique is applied and examined
in detail in the final chapter for the one- and multi-credit case. Exponential as well as
normal importance sampling densities are derived.
Inhaltsverzeichnis (Table of Contents)
- Introduction: Credit Risk and Credit Derivatives
- Modelling Joint Defaults
- The Copula Function Approach
- Default Correlation
- Monte Carlo Simulation
- General Principles and Theoretical Background
- Monte Carlo Approach for Credit Derivatives
- Variance Reduction Techniques for Monte Carlo Methods
- Antithetic Sampling
- Variate Recycling
- Control Variates
- Stratified Sampling
- Conditional Expectation
- Importance Sampling
- Application to Credit Risk
- Basic Variance Reduction Techniques
- Importance Sampling Techniques
- The One Credit Case
- The Two Credit Case
- The n Credit Case
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This paper explores the valuation of credit risk derivatives, focusing on the application of variance reduction techniques within Monte Carlo simulation methods. The work aims to demonstrate how these techniques can enhance the efficiency and accuracy of credit derivative pricing models.
- Credit Risk Derivatives and their Valuation
- Modeling Joint Defaults using Copula Functions
- Monte Carlo Simulation Methods for Credit Derivative Pricing
- Variance Reduction Techniques in Monte Carlo Simulations
- Application of Importance Sampling for Credit Risk Valuation
Zusammenfassung der Kapitel (Chapter Summaries)
- Introduction: Credit Risk and Credit Derivatives: This chapter introduces the concept of credit risk and explores different types of credit risk derivatives, such as credit default swaps and first-to-default baskets. The importance of accurately modeling the joint distribution of credit default times is highlighted as a crucial aspect of credit derivative valuation.
- Modelling Joint Defaults: This chapter focuses on the copula function approach as a method to model the joint distribution of credit default times. The concept of default correlation is discussed in detail, emphasizing its significance in understanding the dependence structure of credit events.
- Monte Carlo Simulation: This chapter provides a comprehensive introduction to the Monte Carlo simulation method, outlining its general principles and theoretical underpinnings. It explains how Monte Carlo simulation can be effectively employed for valuing credit derivatives, focusing on the construction of dependent uniform random variables from dependent normal random variables.
- Variance Reduction Techniques for Monte Carlo Methods: This chapter delves into various variance reduction techniques designed to improve the efficiency of Monte Carlo simulations. It covers methods like antithetic sampling, control variates, stratified sampling, conditional expectation, and importance sampling, providing insights into their implementation and advantages.
- Application to Credit Risk: This chapter examines the practical application of variance reduction techniques to credit risk valuation. It discusses basic variance reduction techniques and provides a detailed analysis of importance sampling techniques, including their application to one-, two-, and n-credit cases.
Schlüsselwörter (Keywords)
The key focus of this paper lies on credit risk, credit derivatives, Monte Carlo simulation, variance reduction techniques, and importance sampling. These concepts are explored in the context of modeling joint defaults using copula functions and analyzing the dependence structure of credit events.
- Quote paper
- Ralph Karels (Author), 2003, Valuing Credit Risk - Variance Reduction Techniques for Monte Carlo Methods, Munich, GRIN Verlag, https://www.grin.com/document/13826