Researcher course in fixed income
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.
Interest rate models price the options embedded in loans, mortgages, callable bonds and swaptions, which make up much of a bank’s derivative book. Unlike a stock, the yield curve is a whole curve that moves, so the models must describe its shape over time without allowing arbitrage. This course takes the main families in turn and calibrates them to market prices.
Why are there so many interest rate models?
Because each trades realism for tractability. Short-rate models are fast and fit today’s curve, but describe its movements crudely. Market models match the quoted prices of caps and swaptions, but are slow to simulate. A rates quant chooses by product, and the course teaches the reasons for each choice.
How is the course taught?
Audio lessons give the reasoning, explainer films show curves evolving under each model, and the workbooks hold derivations, Python notebooks and cheat sheets of the pricing formulas. Assignments and the project receive written feedback from the faculty.
Who is this course for?
Quants heading for rates trading, derivatives pricing or model validation. It counts toward the Certificate in Derivatives Pricing and so toward the Fellowship in Computational Finance.
What you will be able to do
- Price bonds and options under Vasicek, CIR and Hull-White, and fit Hull-White to today's curve.
- Explain the Heath-Jarrow-Morton drift condition and what it implies for any rate model.
- Price caps, floors and swaptions with Black and Bachelier formulas and the market models.
- Calibrate a model to swaption volatilities and explain the effect of the SOFR transition.
Syllabus, module by module
Rates as a random process
Short rate, forward rates and the change of numeraire.
Short-rate models
Vasicek, Cox-Ingersoll-Ross and Hull-White; bond prices and trees.
Heath-Jarrow-Morton
Modelling the whole forward curve and the no-arbitrage drift condition.
Caps, floors and swaptions
Black and Bachelier formulas, normal volatility and negative rates.
Market models
The LIBOR market model, its SOFR successor and simulation of forward rates.
Calibration and exotics
Fitting to the swaption grid and pricing Bermudan and callable products.
How the certificate is earned
Graded assignments and a final project: calibrate Hull-White to a swaption grid and price a Bermudan swaption on a tree. On a pass you receive the Course certificate in Interest Rate Models, issued by the Institute with a verification code. Read how certification works.
Before you start
Stochastic calculus at the Institute's level, and bond pricing and the yield curve.
This course counts toward
- Certificate in Derivatives PricingDerivative pricing in one semester of ten 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.
- Fellowship in Computational FinanceThe top credential on the researcher path. Four semesters, 38 courses, and a dissertation supervised in writing and examined by two faculty members.
Questions applicants ask
Which interest rate model do banks use?
Most desks use Hull-White or a related short-rate model for callable products, and a market model or stochastic-volatility extension for products sensitive to the volatility smile. The course explains why each is chosen.
Does the course cover the end of LIBOR?
Yes. The market models were built on LIBOR forwards; the course shows how they were adapted to compounded overnight rates such as SOFR and what changed for caps and swaptions.