Specialist track, course code DV
Derivatives and Rates
Option pricing from Black-Scholes to stochastic volatility, with the hedging and calibration that make the models useful.
In option pricing, a derivative’s price is the cost of replicating its payoff. That one idea, made precise by Black, Scholes and Merton in 1973, organises the whole subject: the model gives the hedge, the hedge gives the price, and where the model’s assumptions fail the market charges for it through the volatility smile.
What does the derivatives track cover?
The Black-Scholes Model covers the derivation, the formula and its assumptions. Option Greeks covers delta, gamma, vega and theta and how a book is hedged with them. Implied Volatility and the Volatility Smile covers surface construction and what the smile says about the market’s view of risk. The Heston Model, at Researcher level, covers stochastic volatility, pricing by characteristic functions and calibration.
Where does this track lead?
To the Certificate in Derivatives Pricing, on the researcher path, which adds stochastic calculus and ends in a written capstone on model calibration.
Practitioner courses in this track
Lab-based courses. You build, test and cost real strategies and systems on market data.
- 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.
- 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.
- 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.
Researcher courses in this track
Proof-level courses. Stochastic models, estimation theory and the literature behind each method.
Credentials that use this track
- 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.
- 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
Do I need stochastic calculus for derivatives pricing?
For the Practitioner courses, no: Black-Scholes, the Greeks and implied volatility are taught with the formulas and numerical methods. The Certificate in Derivatives Pricing, which sits on the researcher path, requires Stochastic Calculus for Finance.
Are interest rate models covered?
Not yet. Rates courses are in preparation and will be added to this track.