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
  • Advanced structural models

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)
  • Funding value adjustment (FVA)
  • 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

Collateralized Debt Obligations

  • Basics of CDO structure
  • CDO market pricing and risk management
  • Loss Function and CDO Pricing Equation
  • Introduction to Collateralized Debt Obligations (CDO)
  • CDO market pricing and risk management
  • Derive CDO Pricing Equation
  • Introduction to Copula Function
  • Motivation from loss distribution
  • What is Copula Function
  • Classification of Copula Functions
  • Simulating via Gaussian Copula
  • 3 Gaussian Copula Factor mode

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

Correlation Sensitivity and State Dependence

  • The meaning of correlation. Intuition and timescale
  • Linear Correlation and its misuse 
  • Rank Correlation
  • Correlation in exotic options. Equity Structured Product: an example
  • Uncertain correlation model for Mezzanine tranche (best and worst cases)
  • Compound (implied) correlation in Loss Distribution
  • Lessons of correlation sensitivity

Co-intergration: Modeling Long-Term Relationships

  • Multivariate time series analysis
  • Stationary and unit root
  • Vector Autoregression movel (VAR)
  • Co-integrating relationships and their rank
  • Vector Error Correction Model (VECM)
  • Reduced rand model (regression) estimation: Johansen Procedure
  • Stochastic modeling of autoregression: Orstein-Uhlenbeck process
  • Statistical arbitrage using mean reversion
Lecture order and content may occasionally change due to circumstances beyond our control; however this will never affect the quality of the program.