Risk Modelling Course

Lesson 1 • Types of Risk in Organisations

Organisations face credit, market, operational, and liquidity risks. Mapping risk types to business functions contextualises later modelling techniques.

Lesson 2 • Data and Measurement Fundamentals

Model quality depends on data quality. Students evaluate data sources, measurement scales, and common collection biases relevant to risk datasets.

Lesson 3 • Defining Risk in Quantitative Contexts

Risk is defined as a measurable uncertain outcome with consequence. This section establishes the vocabulary and conceptual boundaries used throughout the course.

Lesson 1 • Extreme Value Theory Basics

Tail risk requires specialised tools beyond standard distributions. Block maxima and peaks-over-threshold methods capture rare, high-impact events.

Lesson 2 • Discrete Distributions for Loss Frequency

Frequency models count how often loss events occur. Poisson and negative binomial distributions are fitted to event count data.

Lesson 3 • Parameter Estimation Methods

Accurate parameters are essential for reliable models. Maximum likelihood estimation and method of moments are applied to risk data.

Lesson 4 • Continuous Distributions for Loss Severity

Severity models describe the magnitude of individual losses. Heavy-tailed distributions such as lognormal and Pareto are emphasised.

Lesson 1 • Monte Carlo Simulation for Aggregation

Simulation generates empirical aggregate loss distributions when closed-form solutions are unavailable. Students implement basic Monte Carlo loops for loss aggregation.

Lesson 2 • Reinsurance and Risk Transfer Modelling

Risk transfer structures alter the aggregate loss distribution. Per-occurrence and aggregate stop-loss treaties are modelled analytically and via simulation.

Lesson 3 • Variance Reduction Techniques

Naive simulation is computationally expensive for rare events. Importance sampling and stratified sampling improve tail estimate efficiency.

Lesson 1 • Fitting and Validating Copula Models

Copula selection requires both statistical and domain judgement. Students fit copulas to bivariate loss data and validate using graphical and formal tests.

Lesson 2 • Tail Dependence and Extreme Co-movement

Tail dependence measures the probability of joint extreme losses. Upper and lower tail dependence coefficients are computed for common copulas.

Lesson 3 • Copula Theory and Construction

Copulas separate marginal distributions from dependence structure. Sklar's theorem is stated and applied to construct bivariate risk models.

Lesson 1 • Value-at-Risk Concepts and Computation

VaR quantifies the loss not exceeded at a given confidence level. Historical simulation, variance-covariance, and Monte Carlo VaR methods are compared.

Lesson 2 • Economic Capital Frameworks

Economic capital quantifies the buffer needed to absorb unexpected losses at a target solvency level. Internal models are contrasted with standardised regulatory approaches.

Lesson 3 • Sensitivity Analysis of Risk Measures

Risk measure outputs depend on model assumptions. Sensitivity analysis identifies which inputs drive capital estimates and where model risk is concentrated.

Lesson 4 • Expected Shortfall and Coherent Measures

Expected Shortfall averages losses beyond the VaR threshold and satisfies coherence axioms. Its advantages over VaR for tail risk management are demonstrated.

Lesson 1 • Portfolio Credit Loss Models

Portfolio credit risk arises from correlated defaults. The Gaussian copula credit portfolio model and CreditMetrics framework are implemented.

Lesson 2 • Credit Risk Metrics and Reporting

Credit risk outputs must be translated into management metrics. Expected loss, unexpected loss, and credit VaR are computed and interpreted.

Lesson 3 • Loss Given Default and Exposure

LGD and EAD determine loss magnitude conditional on default. Recovery rate distributions and credit conversion factors are modelled empirically.

Lesson 1 • Operational Risk Loss Distribution Approach

Operational risk uses frequency-severity models applied to internal and external loss data. The loss distribution approach produces regulatory and economic capital estimates.

Lesson 2 • Stress Testing Across Risk Types

Stress tests evaluate model performance under adverse but plausible scenarios. Students design and apply stress scenarios to market and operational risk models.

Lesson 3 • Volatility Modelling and Forecasting

Volatility is time-varying and clusters in financial data. GARCH-family models capture volatility dynamics for use in market risk measurement.

Lesson 4 • Advanced Measurement for Operational Risk

Advanced operational risk models incorporate business environment indicators and control factors. Students adjust loss distributions for qualitative risk assessments.

Lesson 1 • Model Inventory and Documentation

A complete model inventory enables oversight and audit readiness. Documentation standards cover model purpose, assumptions, limitations, and change history.

Lesson 2 • Sources and Types of Model Risk

Model risk arises from incorrect assumptions, data errors, and misuse. A taxonomy of model risk sources guides the design of mitigation controls.

Lesson 3 • Governance Structures and Oversight

Effective governance assigns clear ownership and escalation paths for model issues. Model risk committees, approval workflows, and reporting lines are designed.

Lesson 4 • Model Validation Methodology

Independent validation tests model soundness across development, implementation, and use. Students apply benchmarking, sensitivity testing, and outcome analysis.