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, organizes 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 and the Option Greeks covers the derivation, the formula and its assumptions, then delta, gamma, vega and theta and how a book is hedged with them. Implied Volatility, the Smile and Volatility Trading covers surface construction, what the smile says about the market’s view of risk, and variance swaps and the gap between implied and realized volatility. The Heston Model, at Researcher level, covers stochastic volatility, pricing by characteristic functions and calibration. Options Strategies covers spreads, straddles and collars and what each one bets on.
Where does this track lead?
To the Certificate in Derivatives Pricing, on the researcher path, which adds stochastic calculus, numerical methods and interest rate models 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, 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.
- Options Strategies Options strategies taught the way a professional builds them: from payoff and Greeks, with a view on direction, volatility and time, then sized, tested on history and costed for spreads and assignment.
- 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.
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 Systematic InvestingSeven courses and a capstone on rule-based investing over months and years: asset pricing, trend, factors, carry, allocation and the portfolio construction and risk control that hold them together.
- Certificate in Derivatives PricingDerivative 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.
- Professional Diploma in Algorithmic TradingThe top credential on the practitioner path. Twenty-one courses and an 80-hour capstone covering everything between the mathematics and a book you could defend to a risk committee.
- Fellowship in Computational FinanceThe top credential on the researcher path. Twenty-one courses and a dissertation supervised in writing and 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 and Stochastic Differential Equations.
Are interest rate models covered?
Yes. Bond Pricing, Yield Curves and Mortgage-Backed Securities and Interest Rate Models sit in the fixed income track and both count toward the Certificate in Derivatives Pricing.