Specialist track, course code QF
Quantitative Foundations
The mathematical finance every later course assumes: probability, statistics, linear algebra, time series and stochastic calculus, taught with market data rather than textbook urns.
Every model in trading and risk rests on a small set of tools from mathematical finance. A volatility forecast is a time series model. A Value at Risk number is a quantile of a probability distribution. An option price is an expectation under a change of measure. A portfolio weight is the solution of a constrained optimization. Learn these tools once, properly, and every later course reads as an application rather than a new subject.
What does the Quantitative Foundations track cover?
The track runs from a free introduction to quantitative finance through three Foundation courses (mathematics with linear algebra, probability with statistics, and how markets and their instruments work) to Researcher courses in stochastic calculus with stochastic differential equations, GARCH models with hidden Markov regimes and Bayesian methods, and numerical methods. Time series analysis and financial econometrics sit together at Practitioner level, because they are used directly in trading research.
Who is this track for?
Engineers and scientists who know mathematics but not its financial use; finance graduates whose statistics stopped at regression; and anyone heading for the researcher path, where the Fellowship in Computational Finance builds on these courses.
Open courses in this track
Free primers. Read, watch and work the exercises before you spend anything.
- Introduction to Quantitative Finance What is quantitative finance? A free primer on what the field is, what quants actually do in banks, funds and trading firms, and what you need to learn to join them.
- Monte Carlo Simulation, From First Principles What is a Monte Carlo simulation? A free course that builds one from first principles: random numbers, the law of large numbers, simulated price paths and their error bars.
Foundation courses in this track
The mathematics, statistics, data and market knowledge every later course assumes.
- Financial Markets and Instruments A financial markets course for people who will build models of markets: what each instrument is, who trades it, where and how it trades, and what happens between the click and the settled position.
- Mathematics for Quantitative Finance: Calculus and Linear Algebra The calculus, linear algebra, optimization and differential equations that pricing, risk and portfolio models are built on, revised and applied to finance. It also teaches the linear algebra for finance behind portfolios and factor models.
- Probability for Quantitative Finance, with Statistics The probability every quant course assumes: distributions, expectation, conditioning and the limit theorems, with each idea tested on real return data. It also teaches the statistics for finance that every model rests on.
Practitioner courses in this track
Lab-based courses. You build, test and cost real strategies and systems on market data.
Researcher courses in this track
Proof-level courses. Stochastic models, estimation theory and the literature behind each method.
- 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.
- Numerical Methods in Finance The numerical methods behind every pricing and risk system: Monte Carlo and its variance reduction, finite differences for pricing equations, lattices, Fourier methods, root finding and optimization for calibration, with attention to error and stability.
- Stochastic Calculus and Stochastic Differential Equations Brownian motion, the Ito integral, Ito's lemma, change of measure and martingale pricing, derived carefully and applied to the models used on derivatives desks. It also teaches stochastic differential equations and how to solve them.
Credentials that use this track
- Foundation Certificate in Computational FinanceThe entry quantitative finance certificate, and the opening stage of both the Professional Diploma and the Fellowship. Six courses that settle the mathematics, statistics, data and market knowledge every later course assumes, closed by a capstone.
- Certificate in Algorithmic TradingSeven courses and a capstone that take a strategy from idea to a costed, sized and validated system, traded on paper and reported the way a trading desk would read it.
- 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 Portfolio ManagementSeven courses and a capstone on building portfolios with numbers: mean-variance and its failures, robust optimization, Black-Litterman views, factors, asset allocation, bonds, attribution and risk.
- 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 Derivatives PricingDerivative pricing in seven courses and a capstone, from stochastic calculus to stochastic volatility and interest rate models: how options are priced, hedged, traded and calibrated to the market.
- 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.
- Professional Diploma in Algorithmic TradingThe top credential on the practitioner path. Twenty-one courses and an 80-hour capstone covering everything between the mathematics and a book you could defend to a risk committee.
- 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
How much mathematics do I need for quantitative finance?
For practitioner work: probability, statistics, linear algebra and enough calculus to follow an optimization. For derivatives pricing and research: stochastic calculus and differential equations as well. The Foundation courses cover the first group; the Researcher courses cover the second.
Can I skip the Foundation courses?
Yes, if you already have the material. Each Foundation course lists its outcomes; if you can already do every item on the list, start at the level above.