Credential program on the researcher path
Certificate in Derivatives Pricing
Derivative pricing in five courses and a capstone, from stochastic calculus to stochastic volatility: how options are priced, hedged 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; and the Heston model, its calibration and its numerical pricing.
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 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.
- 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.
- 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.
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].
- 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.
- 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 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.
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.
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
How much mathematics is needed?
Calculus, linear algebra and probability at undergraduate level. Stochastic Calculus for Finance 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?
Not yet. Rates courses are in preparation. This program covers equity and index options.
How long does the certificate take?
154 hours of study. At eight hours a week, about five months.