Researcher course in quantitative foundations
ARCH and GARCH Volatility Models
The GARCH model and its family, from Engle's original ARCH to asymmetric and multivariate GARCH: derivation, maximum likelihood estimation, diagnostics and forecasting.
Volatility comes in clusters: a large move today makes a large move tomorrow more likely. Robert Engle’s ARCH model of 1982 and Tim Bollerslev’s GARCH model of 1986 turned that observation into equations that can be estimated and forecast, and the family remains the standard tool for volatility forecasting in risk management.
Why study GARCH at researcher level?
Because using a GARCH library is easy and using it well is not. Persistence close to one, fat-tailed residuals, asymmetric responses and structural breaks all change the forecasts, and the choice between specifications is a judgement that needs the theory behind it.
Who is this course for?
Risk modellers, volatility traders and researcher-path students. It counts toward the Certificate in Quantitative Risk Management and the Fellowship in Computational Finance.
What you will be able to do
- Derive the properties of ARCH and GARCH processes, including stationarity conditions.
- Estimate GARCH models by maximum likelihood and check them with standardised residuals.
- Fit asymmetric models such as EGARCH and GJR-GARCH and test for leverage effects.
- Forecast volatility at several horizons and evaluate the forecasts.
- Use GARCH forecasts in value at risk and in volatility-targeted position sizing.
Syllabus, module by module
Volatility clustering
The stylised facts and Engle's 1982 ARCH model.
GARCH(1,1)
Bollerslev's generalisation, stationarity, persistence and the unconditional variance.
Estimation
Maximum likelihood with normal and Student t errors, and quasi-maximum likelihood.
Diagnostics
Standardised residuals, Ljung-Box and ARCH-LM tests, and news impact curves.
Asymmetry
EGARCH and GJR-GARCH, and the leverage effect in equity markets.
Forecasting
Multi-step forecasts, realised volatility as a benchmark and forecast evaluation.
Multivariate GARCH
Constant and dynamic conditional correlation models for portfolios.
Applications
GARCH in value at risk, option pricing and volatility targeting.
How the certificate is earned
A written, paper-style assessment: derivations, estimation of competing GARCH specifications on two markets, a forecast comparison and a discussion of model risk. On a pass you receive the Course certificate in ARCH and GARCH Volatility Models, issued by the Institute with a verification code. Read how certification works.
Before you start
Time series analysis at the level of Time Series Analysis for Finance, and maximum likelihood estimation.
This course counts toward
- Certificate in Quantitative Risk ManagementA financial risk management certification in five courses and a capstone on measuring and governing market risk: VaR and expected shortfall, volatility models, stress tests and the validation of the models themselves.
- Fellowship in Computational FinanceThe top credential on the researcher path. Nine courses, eight of them at researcher level, and a supervised dissertation, examined by two faculty members.
Questions applicants ask
What is a GARCH model used for?
Forecasting volatility. Risk managers use it for value at risk, traders for position sizing and option desks as a reference for implied volatility.
Which software is used?
Python with the arch library, plus estimation code written from scratch so you see what the library does.