Valuing Credit Risk - Variance Reduction Techniques for Monte Carlo Methods

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.