Pricing and hedging interest rate products is a very common task for practitioners in mathematical finance. The course conveys the pertinent methods that are currently in use in the financial industry. It will cover both practical aspects, such as market conventions, and the theoretical underpinnings of the models.

We will briefly present plain vanilla interest rate products, like bonds, caps, swaps, and swaptions. To price more involved structures, models for the evolution of the yield curve are required. After a short presentation of the Hull White model, the bulk of the course will deal with the LIBOR Market Model. This is in fact a whole family of models, as there are numerous ways to model volatility and correlation, and to calibrate the model. Its numerical realization involves the discretization of stochastic differential equations, possibly in conjunction with variance reduction. We will also consider the numerically demanding pricing of exotic trades with early exercise features.

Oral exam

Brigo, Mercurio: Interest Rate Models - Theory and Practice Glasserman: Monte Carlo Methods in Financial Engineering