Libor Market Model: Single & Multi-Factor

Most fixed-income courses stop at the theory. This one does not. You start from a discount curve and a set of caplet volatilities and finish with a working Monte Carlo engine that prices real interest-rate derivatives — the same workflow used on a rates desk.

You will build two models: a single-factor LIBOR Market Model, where every forward rate is driven by one Brownian motion, and a multi-factor model that introduces a realistic correlation structure through three principal-component factors. Both are then put to work inside a Monte Carlo simulation.

Every result is checked. The market data and benchmark prices come from Pietro Veronesi's Fixed Income Securities (pp. 722–726 and 779), so at each step you can verify your implementation against published, peer-reviewed numbers — no guessing whether your code is right.

The course is built around one end-to-end project. You begin with a quarterly discount curve, quoted forward rates, and a volatility structure, and you implement the plumbing yourself: zero-coupon bond pricing, continuously-compounded spot and forward rates, swap valuation, and cubic-spline interpolation.

From there you calibrate and simulate the single-factor LMM using caplet forward volatilities, then build the multi-factor LMM using forward-rate and three-factor PCA volatilities. Finally you use both models in a Monte Carlo setting to price two derivatives: an option on a zero-coupon bond and a receiver swaption.

You finish by comparing single- versus multi-factor prices, benchmarking both against Veronesi's reported values, and discussing where each model is appropriate — and how to make the code production-fast.