# Module 5: Credit Products and Risk

### Introduction to Credit Derivatives & Structural Models

• Introduction to credit risk
• Modelling credit risk
• Basic structural models: Merton Model, Black and Cox Model

### Intensity Models

• Modelling default by Poisson Process
• Relationship between intensity and arrival time of default
• Risky bond pricing: constant vs. stochastic hazard rate
• Bond pricing with recovery
• Theory of affine models
• Affine intensity models and use of Feynman-Kac
• Two-factor affine intensity model example: Vasicek

### Credit Default Swaps

• An Introduction to CDS
• Default Modelling Toolkit. Inhomogenous Poisson Process
• CDS Pricing: Basic and Advanced Models
• Bootstrapping intensity from CDS market quotes
• Accruals and upfront premium in CDS pricing

### X-Valuation Adjustment (CVA, DVA, FVA, MVA) Theory

• Historical development of OTC derivatives and xVA
• Credit and debt value adjustments (CVA and DVA)
• Margin and Capital Value Adjustments (MVA and KVA)
• Current market practice and application

### X-Valuation Adjustment (CVA, DVA, FVA, MVA) Implementation

• Implementation of counterparty credit valuation adjustment (CVA)
• Review the numerical methodologies currently used to quantify CVA in terms of exposure and Monte Carol simulation and the Libor Market Model
• Illustrate this methodology as well as DVA, FVA and others

### CDO & Correlation Sense

• CDO market pricing and risk management
• Loss Function and CDO Pricing Equation
• Motivation from loss distribution
• What is Copula Function
• Classification of Copula Functions
• Simulating via Gaussian Copula
• 3 Gaussian Copula Factor mode
• The meaning of correlation. Intuition and timescale
• Linear Correlation and its misuse
• Rank Correlation
• Correlation in exotic options
• Uncertain correlation model for Mezzanine tranche
• Compound (implied) correlation in Loss Distribution

### Statistical Methods in Estimating Default Probability

• Sources of default probability information
• Capital Structure Arbitrage
• Generalized Linear Models (GLM): theory, estimation and inference
• Exponential family of distributions
• Logit and probit regressions. Link functions
• Estimation of default probability for an enterprise with a logit model
• Sovereign credit rating transitions and the ordered probit model