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 optimisation. 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 (probability, statistics and the core mathematics) to Researcher courses in stochastic calculus, stochastic differential equations, GARCH volatility models and hidden Markov regime models. Time series analysis sits at Practitioner level because it is 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
Short courses that fix the mathematics, statistics and code every later course assumes.
- Mathematics for Quantitative Finance The calculus, linear algebra, optimisation and differential equations that pricing, risk and portfolio models are built on, revised and applied to finance.
- Probability for Quantitative Finance The probability every quant course assumes: distributions, expectation, conditioning and the limit theorems, with each idea tested on real return data.
- Statistics for Finance and Trading Estimation, testing and regression for financial data, with the traps that make trading research go wrong: dependence, fat tails and testing too many ideas.
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.
- 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.
- Hidden Markov Models for Market Regimes Regime-switching models for markets: hidden Markov models, their algorithms and estimation, and how to use inferred regimes without fooling yourself.
- Stochastic Calculus for Finance 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.
- Stochastic Differential Equations for Finance How stochastic differential equations are solved, simulated and estimated, with the mean-reverting, short-rate and volatility models that use them.
Credentials that use this track
- Foundation Certificate in Computational FinanceThe entry quantitative finance certificate. Four Foundation courses that fix the probability, statistics and Python every later course assumes, and a first look at how trading systems are built.
- Certificate in Statistical ArbitrageFive courses and a capstone on market-neutral trading: time series foundations, pairs and baskets, cointegration and the validation that keeps spread strategies honest.
- 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.
- Certificate in Derivatives PricingDerivative pricing in five courses and a capstone, from stochastic calculus to stochastic volatility: how options are priced, hedged and calibrated to the market.
- Certificate in Machine Learning for TradingFive courses and a capstone on applying machine learning to markets without fooling yourself: labelling, features, purged validation, overfitting tests and reinforcement learning.
- 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
How much mathematics do I need for quantitative finance?
For practitioner work: probability, statistics, linear algebra and enough calculus to follow an optimisation. 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.