Credential program on the researcher path
Certificate in Derivatives Pricing
Derivative 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.
An option price is a statement about future volatility, and a hedge is a bet that the statement is right. The Certificate in Derivatives Pricing builds the mathematics of derivative pricing that makes both precise: stochastic calculus, risk-neutral pricing, the Black-Scholes model and the stochastic volatility models that replaced it on trading desks.
What does the certificate cover?
Brownian motion, Ito’s lemma and stochastic differential equations; Black-Scholes by replication and by risk-neutral expectation; the Greeks and dynamic hedging; implied volatility and the smile; the Heston model and its calibration; the numerical methods that price what has no formula, from finite differences to Monte Carlo; yield curves and interest rate models; and volatility as a traded asset.
Who is it for?
Quantitative researchers and analysts on derivatives desks, graduate students preparing for quant roles, and engineers who maintain pricing libraries and want to understand them.
The courses in this program
- 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.
- The Black-Scholes Model and the Option Greeks 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. It also teaches the option Greeks and hedging with them.
- Implied Volatility, the Smile and Volatility Trading 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. It also teaches volatility trading: variance swaps, straddles and the volatility risk premium.
- 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.
- 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.
- Interest Rate Models The models banks use to price options on interest rates: short-rate models from Vasicek to Hull-White, the Heath-Jarrow-Morton framework, the market models behind caps and swaptions, the move from LIBOR to SOFR, and calibration to market prices.
- Bond Pricing, Yield Curves and Mortgage-Backed Securities Bond pricing and the yield curve from first principles to desk practice: price and yield, duration and convexity, bootstrapping and fitting curves, carry and roll-down, and hedging a bond portfolio's interest rate risk. It also teaches mortgage-backed securities and prepayment risk.
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.
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: the academy office.
- Python and SQL 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. It also teaches SQL for finance, so your data lives in a database rather than in files.
- 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.
- 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.
- 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.
What is the derivatives capstone?
You calibrate a stochastic volatility model to a listed option surface, price and hedge a path-dependent derivative under it, and compare the hedging error with Black-Scholes hedging on the same data. The submission is a paper-style report with derivations, code and a discussion of where the model fails.
What does the credential record?
It records that you passed the proctored exam of every course listed on this page and the capstone, assessed by the Institute's faculty. The credential is issued by the Institute. Each one carries a verification code that an employer can check with the credentials office.
Questions applicants ask
How much mathematics is needed?
Calculus, linear algebra and probability at undergraduate level. Stochastic Calculus and Stochastic Differential Equations is part of the program and builds Ito calculus from there. Mathematics for Quantitative Finance is the right preparation if any of these are rusty.
Does the program cover interest rate derivatives?
Yes. Bond Pricing, Yield Curves and Mortgage-Backed Securities, and Interest Rate Models, are part of the program, from curve building to short-rate models and the LIBOR market model.
How long does the certificate take?
76 hours of material across the seven courses, each hour with its audio edition and workbook, and a capstone of 20 hours of your own work. The license runs 12 months, so you set the pace around a job.