COMMERICAL AND INDUSTRIAL MATHEMATICS
November 24, 2024

QUANTITATIVE METHODS FOR CREDIT RISK MANAGEMENT


May 15-16, 2000

INSTRUCTOR:
Dr. Dan Rosen
Director of Research, Algorithmics Inc.

COURSE OVERVIEW

WHAT YOU WILL LEARN
1. Pricing Models of Credit Risky Instruments and Derivatives

  • Introduction

    - no arbitrage models & risk measurement models - structural & reduced form models
  • Merton's model based on the value of the firm & extensions
  • Jarow-Turnbull family: Jarow-L&o-Turnbull, Das-Tuffano, Jarow-Turnbull integrated model
  • Duffie-Singleton model


2. Counter Party Exposure for Derivative Portfolios
  • Basic Concepts
  • Monte Carlo methods
    - multi-factor long term statistical models: estimation & simulation - dynamic simulation of collateral & credit mitigation techniques
  • "Wrong way" exposures: conditional models of credit exposures that are correlated to the market
  • Exposures of credit derivatives (conditional on credit states)
  • Systematic stress testing of exposures & rollover risk - the scenario b&ing approach

3. Portfolio Credit Risk Models
  • Basic principles: conditional credit events & an integrated framework for portfolio credit risk models
  • The analytical frameworks of CreditRisk+, CreditMetrics, KMV, CreditPortfolioView
  • Integrated market & credit risk portfolio model (Iscoe-Kreinin-Rosen)
  • Advanced analytical & Monte Carlo techniques in portfolio credit risk:
    -application of the Law of Large Numbers, Central Limit Theorem, Probability & Moment generating functions
  • Statistical estimation issues of portfolio credit risk models

4. Credit Risk Management & Optimization Tools
  • Limitations of volatility & mean-variance models
  • Scenario based risk management tools
  • marginal risk, risk contributions, best hedges, risk decomposition
  • Stochastic scenario optimization tools
    -Mathematical Programming formulations with coherent risk measures: regret & expected shortfall

COURSE FACULTY

Dr. Dan Rosen is Director of Research at Algorithmics Inc. In this role, he is responsible for the company's financial & mathematical research, as well as joint projects with academic institutions.

Dr. Rosen joined Algorithmics in 1995. He has headed the design of various market risk management tools, credit risk methodologies, advanced simulation & optimization techniques, as well as their application to several industrial settings. Dr. Rosen is also one of the founders of RiskLab, a network of research centers in Mathematics & Computational Finance, initiated by Algorithmics & the Univ. of Toronto.

Prior to joining Algorithmics, he was a research associate at the University of Toronto's Centre for Management of Technology, where he initiated & coordinated the Performance Analysis Research Program for the Financial Services Industry.

He holds several degrees, including a M.A.Sc. & Ph.D. in Applied Sciences from the University of Toronto. Dr. Rosen has authored numerous papers on applied mathematics & operations research applications to banking & finance, & lectures extensively on market & credit risk & financial engineering.