Interconnected Risks: Quantitative Risk Management with Copulas Training Course

Introduction

In modern finance, accurately quantifying risk, especially in portfolios of interdependent assets, is a complex challenge. Traditional approaches often rely on linear correlation, which fails to capture the intricate, non-linear dependencies, particularly during extreme market events or tail risks. The underestimation of these dependencies was a key factor in the global financial crisis. Copulas offer a sophisticated and flexible mathematical tool to overcome these limitations by allowing the separation of marginal distributions from the dependence structure, providing a more realistic and robust assessment of joint probabilities of adverse outcomes.

This intensive training course is meticulously designed to equip participants with a comprehensive and practical understanding of quantitative risk management using copulas. From mastering the theoretical underpinnings of copulas and their various families to applying them in real-world scenarios for portfolio risk, credit risk, and operational risk aggregation, you will gain the expertise to build more accurate and robust risk models. This empowers you to enhance your institution's risk measurement capabilities, comply with regulatory requirements, and make more informed strategic decisions in an increasingly volatile and interconnected financial landscape.

Target Audience

  • Quantitative risk managers and analysts in banks, insurance companies, and asset management firms.
  • Financial engineers and model validators.
  • Portfolio managers and traders.
  • Academics and graduate students (Master's and PhD) in quantitative finance, financial mathematics, or econometrics.
  • Professionals involved in credit risk modeling, operational risk, and integrated risk management.
  • Statisticians and data scientists working with complex dependence structures.
  • Regulatory compliance officers.
  • Actuaries and insurance professionals.

Duration: 10 days

Course Objectives

Upon completion of this training course, participants will be able to:

  • Understand the limitations of traditional correlation measures in financial risk management.
  • Grasp the theoretical foundations of copulas, including Sklar's Theorem.
  • Analyze various families of copulas (elliptical, Archimedean) and their properties (e.g., tail dependence).
  • Comprehend the process of selecting and fitting appropriate copula models to financial data.
  • Evaluate the application of copulas in measuring Value-at-Risk (VaR) and Expected Shortfall (ES) for multi-asset portfolios.
  • Develop practical skills in implementing copula-based risk models using statistical software (e.g., R, Python).
  • Navigate the challenges of high dimensionality, model selection, and validation in copula modeling.
  • Formulate robust risk assessment and aggregation strategies using copula techniques for market, credit, and operational risks.

Course Content

  1. Limitations of Traditional Risk Measures and Correlations
  • Review of standard risk measures: Value-at-Risk (VaR) and Expected Shortfall (ES)
  • The role of correlation in portfolio risk: limitations of linear correlation (Pearson coefficient)
  • Why traditional correlation fails during market downturns (e.g., non-normality, tail dependence)
  • Introduction to concepts of dependence beyond linear correlation
  • The need for flexible tools to model multivariate distributions
  1. Introduction to Copulas: Fundamentals
  • What is a copula? Definition and intuition
  • Sklar's Theorem: separating marginals from dependence structure
  • Properties of copulas: invariance under monotonic transformations, Fréchet-Hoeffding bounds
  • Examples of basic copulas: independence copula, comonotonic copula, countermonotonic copula
  • Heuristic understanding of copula functions in modeling dependencies
  1. Measures of Dependence and Tail Dependence
  • Kendall's Tau and Spearman's Rho: rank correlation coefficients
  • Comparison of linear correlation with rank correlations
  • Concept of tail dependence: upper and lower tail dependence
  • Why tail dependence is crucial in financial risk management
  • How different copulas capture different types of tail dependence
  1. Families of Copulas: Elliptical Copulas
  • Gaussian copula: properties, estimation, and limitations (no tail dependence)
  • Student's t-copula: capturing heavy tails and symmetric tail dependence
  • Parameter estimation for elliptical copulas
  • Simulating from Gaussian and Student's t-copulas
  • Applications and misapplications of the Gaussian copula (e.g., CDOs crisis)
  1. Families of Copulas: Archimedean Copulas
  • Introduction to Archimedean copulas: construction using generators
  • Popular Archimedean families: Clayton, Gumbel, Frank
  • Properties of Archimedean copulas: asymmetric tail dependence (Clayton for lower, Gumbel for upper)
  • Parameter estimation for Archimedean copulas
  • Simulating from Archimedean copulas
  1. Copula Selection and Goodness-of-Fit Tests
  • Visual inspection: scatter plots of pseudo-observations
  • Information criteria for model selection: AIC, BIC
  • Goodness-of-fit tests for copulas: graphical tests, statistical tests (e.g., White test, bootstrap methods)
  • Copula model risk: the importance of accurate model selection
  • Practical considerations in choosing the "best" copula
  1. Copulas in Portfolio Risk Management
  • Aggregating risks with copulas: from individual marginal distributions to portfolio loss distribution
  • Calculating portfolio VaR and ES using copula-based simulations
  • Risk contributions of individual assets to portfolio risk
  • Scenario analysis and stress testing with copulas
  • Diversification benefits under different dependence structures
  1. Copulas in Credit Risk Modeling
  • Modeling default dependencies: why correlation is insufficient
  • Applications in Credit Default Swaps (CDS) and Collateralized Debt Obligations (CDOs) pricing
  • Joint default probabilities using copulas
  • From individual obligor default probabilities to portfolio credit losses
  • Credit risk models incorporating copulas (e.g., Vasicek model with copula extensions)
  1. Copulas in Operational Risk and Integrated Risk Management
  • Aggregating operational losses from different business lines or event types
  • Modeling dependencies between market, credit, and operational risks for integrated risk management
  • Capital aggregation using copulas for regulatory capital (e.g., Solvency II, Basel III)
  • Challenges and benefits of using copulas for enterprise-wide risk management (ERM)
  • Incorporating expert judgment into copula modeling for sparse data
  1. Advanced Topics and Implementation
  • High-dimensional copulas: challenges and recent advances (e.g., Vine Copulas)
  • Time-varying copulas: modeling dynamic dependence structures
  • Copulas with extreme value theory (EVT): combining tails with dependence
  • Implementing copula models in R or Python (e.g., copula package in R, copulas library in Python)
  • Case studies and real-world applications of copulas in financial institutions.

CERTIFICATION

  • Upon successful completion of this training, participants will be issued with Macskills Training and Development Institute Certificate

TRAINING VENUE

  • Training will be held at Macskills Training Centre. We also tailor make the training upon request at different locations across the world.

AIRPORT PICK UP AND ACCOMMODATION

  • Airport pick up and accommodation is arranged upon request

TERMS OF PAYMENT

Payment should be made to Macskills Development Institute bank account before the start of the training and receipts sent to info@macskillsdevelopment.com

For More Details call: +254-114-087-180

 

Interconnected Risks: Quantitative Risk Management With Copulas Training Course in Kenya
Dates Fees Location Action