Credential program on the researcher path
Fellowship in Computational Finance
The top credential on the researcher path. Nine courses, eight of them at researcher level, and a supervised dissertation, examined by two faculty members.
The Fellowship in Computational Finance trains research, not routine. Its courses are taught at proof level: you derive the models before you use them, estimate them on data, and study the literature that shows where they fail. The dissertation then asks you to do the same for a question of your own.
What does the Fellowship cover?
The mathematics of quantitative finance; stochastic calculus and stochastic differential equations; volatility models from GARCH to Heston; hidden Markov models for regimes; cointegration; Bayesian portfolio construction with Black-Litterman; and the methods of financial machine learning.
Who is it for?
Quantitative researchers who want formal training, graduate students preparing for research roles, and practitioners with a question they have wanted to study properly. Applicants should be comfortable with university calculus, linear algebra and probability.
The courses in this program
- 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.
- 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.
- 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 Volatility and the Heston Model Stochastic volatility in depth: why volatility needs its own process, the Heston model and its characteristic function, Fourier pricing methods, calibration to a volatility surface, simulation schemes, and rough volatility in outline.
- Financial Machine Learning The research methods developed for machine learning on financial data: sampling with information-driven bars, triple-barrier labels and meta-labeling, sample weights for overlapping outcomes, purged cross-validation, feature importance, and statistics of backtest overfitting.
- Cointegration Models for Spread Trading The econometrics behind spread trading: unit roots, Engle-Granger and Johansen cointegration tests, vector error correction models, baskets of more than two assets, and optimal entry and exit for an Ornstein-Uhlenbeck spread.
- The Black-Litterman Model The Black-Litterman model in full: reverse optimisation to implied equilibrium returns, expressing views, the Bayesian combination and its derivation, the choice of tau and the view uncertainty matrix, and extensions to views on factors.
What should you know before you start?
The courses in this program build on the courses below. They are not part of the program and not included in its price. If you have not studied this material, take them first. Admissions can tell you whether your background already covers them: [email protected].
- Modern Portfolio Theory Markowitz's framework from first principles: expected return and covariance, the benefit of diversification, the efficient frontier, the minimum variance and tangency portfolios, and the capital market line, all computed in Python.
- Python for Finance A Python for finance course with the Python every later course assumes: loading and cleaning market data with pandas, computing returns and risk with NumPy, plotting, and writing code another person can rerun.
- 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.
- The Black-Scholes Model Option pricing from the ground up: payoffs and no-arbitrage bounds, the binomial model, the replication argument, the Black-Scholes equation and formula, risk-neutral valuation, and numerical pricing in Python.
- Option Greeks The sensitivities that options traders manage: delta, gamma, vega, theta and rho, how they behave across strikes and time, delta and gamma hedging, the link between gamma and theta, and hedging a book in simulation.
- Implied Volatility and the Volatility Smile What option prices say about expected volatility: solving for implied volatility, the smile and skew, the term structure, building and fitting a volatility surface, and the no-arbitrage conditions a surface must satisfy.
- Machine Learning for Trading Applying machine learning to trading problems without fooling yourself: building features and labels from market data, linear, tree and neural network models, time-series cross-validation, feature importance, and turning predictions into a tested strategy.
- Portfolio Optimization Portfolio construction that survives real data: estimating covariance with shrinkage, constrained and robust optimisation, risk budgeting and risk parity, hierarchical risk parity, and the costs of rebalancing.
- Time Series Analysis for Finance The time series methods behind trading signals and risk forecasts: stationarity, autocorrelation, ARMA models, unit roots, volatility clustering and honest forecast evaluation.
- Pairs Trading and Mean Reversion The pairs trade from selection to testing: how to find candidate pairs, the distance and cointegration methods, hedge ratios, spread z-scores, trading rules, and the reasons pairs stop working.
How does the Fellowship dissertation work?
You propose a research question in computational finance, agree its scope with a faculty supervisor, and write a dissertation of 10,000 to 15,000 words with reproducible code and data. Supervision runs to six one-to-one meetings by video. The dissertation is examined by two faculty members, one of whom did not supervise it, and ends in a recorded oral examination.
Is this credential accredited?
No. It is an unaccredited Institute credential. It records that you passed every assessed component listed on this page, marked by the Institute's faculty. It is not a university degree and is not issued by Carnegie Mellon University. Each credential carries a verification code that an employer can check with [email protected].
Questions applicants ask
Is the Fellowship a master's degree?
No. It is an unaccredited Institute credential, not a degree, not academic credit and not issued by Carnegie Mellon University. It is designed for people who want research training in computational finance without enrolling in a degree program.
Who supervises the dissertation?
A member of the Institute’s faculty, matched to the topic you propose. The question must fall within the faculty’s areas of expertise; the supervisor confirms this before you start.
How long does the Fellowship take?
380 hours of study, including the dissertation. At eight hours a week, about a year.