Researcher course in quantitative foundations
GARCH Models, Market Regimes and Bayesian Methods
The GARCH model and its family, from Engle's original ARCH to asymmetric and multivariate GARCH: derivation, maximum likelihood estimation, diagnostics and forecasting. It also teaches hidden Markov models for market regimes and Bayesian statistics for estimation under uncertainty.
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 judgment that needs the theory behind it.
What is a hidden Markov model used for in trading?
Markets behave differently in different periods: calm rising markets, volatile falling ones, and long sideways stretches. A hidden Markov model treats these as unobserved states that switch according to fixed probabilities, and infers from returns which state the market is likely in.
Detecting volatility regimes for risk scaling, switching between strategies that work in different conditions, and modeling the dynamics of spreads and interest rates. The most common mistake is using smoothed probabilities, which use future data, in a backtest; the course spends a module on avoiding it.
Where is it used on a desk?
Bayesian statistics is a way to estimate with too little data, and in finance there is never enough. Ten years of monthly returns is 120 numbers, which says little about an expected return. Bayesian methods combine the data with a prior, shrink unstable estimates toward something sensible, and report what is still uncertain.
In shrinkage of covariance matrices for portfolio construction, in Black-Litterman views, in regime and state-space models, in judging which of many strategies is genuinely better, and in machine learning models that need calibrated uncertainty. The course works each of these on real data.
Who is this course for?
Risk modelers, volatility traders and researcher-path students.
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 standardized residuals.
- Fit asymmetric models such as EGARCH and GJR-GARCH and test for leverage effects.
- Forecast volatility at several horizons and evaluate the forecasts.
- Specify a hidden Markov model for returns and explain each parameter.
- Set priors, compute posteriors and explain how they combine judgment with data.
Syllabus, module by module
Volatility clustering
The stylized facts and Engle's 1982 ARCH model.
GARCH(1,1)
Bollerslev's generalization, stationarity, persistence and the unconditional variance.
Estimation
Maximum likelihood with normal and Student t errors, and quasi-maximum likelihood.
Diagnostics
Standardized residuals, Ljung-Box and ARCH-LM tests, and news impact curves.
Regimes in markets
Evidence for distinct market states and Hamilton's 1989 regime-switching model.
Bayes' rule at work
Priors, likelihoods and posteriors on simple financial questions.
What every course contains
Every paid course comes with the first seven and the certificate, whichever level it sits at. The proctored exam and the credential come when the course is taken as part of a Certificate, Diploma or Fellowship. Everything is self-paced: the material is yours to study in any order, at any hour, for the whole of the license.
- Workbooks. Written to train the thinking patterns and the important concepts of the course, with worked problems and the reasoning behind each answer, so that you learn to think the way the subject is thought.
- Audio edition. Focused, well-presented recordings with explainers and examples of the material, made to be interesting, relevant and entertaining, so that the general subject can be learned away from the desk.
- Notes. Pre-produced notes with every fact the course relies on, written out in full, so that nothing has to be transcribed from the films or the audio.
- Cheat sheet. One sheet with every important learning concept of the course on it, to keep beside you during the work and to revise from before the exam.
- Named sources. Every fact in the notes names its source, the paper, the book or the dataset, for anyone who wants to dig in further.
- Explainer films. Focused films, in the style of the sample films on the catalog page, that walk through the most difficult concepts of the course with visual explanations of a high standard.
- Transcript. A full transcript of every film and every audio recording, searchable and quotable.
- Proctored exam. Taken as part of a Certificate, Diploma or Fellowship, the course ends in a proctored multiple-choice questionnaire, with a pass mark of 60% and three retakes included. A course taken on its own is assessed by its coursework and has no exam.
- Verifiable certificate. A certificate of completion that a third party can verify: an employer sends the code on it to the credentials office and receives written confirmation of the course, the date and the result.
- Credential of the program. The Certificate, Diploma or Fellowship of the program, track or path the course belongs to, awarded when every course in it is passed. Which one depends on the program you choose.
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 GARCH Models, Market Regimes and Bayesian Methods, issued by the Institute with a verification code. A course taken as part of a Certificate, Diploma or Fellowship ends in a proctored online exam with a pass mark of 60%. The fee includes three retakes; each attempt after that carries a reduced proctored exam fee. A course taken on its own is assessed by its coursework and has no exam. Read how certification works.
Before you start
This course assumes the material of the courses below, or the same knowledge gained elsewhere.
This course counts toward
- Certificate in Statistical ArbitrageSeven courses and a capstone on market-neutral trading: time series foundations, pairs and baskets, cointegration, regimes, costs and the validation that keeps spread strategies honest.
- Certificate in Quantitative Risk ManagementA financial risk management certification in six courses and a capstone on measuring and governing market and credit risk: VaR and expected shortfall, volatility models, stress tests, credit and counterparty risk, bank capital and the validation of the models themselves.
- Certificate in Machine Learning for TradingFive courses and a capstone on applying machine learning to markets without fooling yourself: labeling, features, purged validation, deep and language models, regimes and reinforcement learning.
- Fellowship in Computational FinanceThe top credential on the researcher path. Twenty-one courses and a dissertation supervised in writing and 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.
Can a hidden Markov model detect a bear market in advance?
No model knows in advance. An HMM estimates the probability that the market is already in a given regime, using data up to today. The course measures how quickly that estimate reacts, which is the honest test.
Why use Bayesian statistics in finance?
Because financial data is short and noisy, and sample estimates of means and covariances are unstable. Bayesian methods add structure through priors and shrinkage, and they keep the uncertainty in the answer instead of hiding it.