TAs: -

This course will convey the basic concepts and analytical methodology for interest rate modeling, term structure calibration and the valuation of fixed income securities and interest rate derivatives.

Students should have prior knowledge of probability theory, stochastic calculus, and derivatives valuation.

100% final exam (open book)

There is no required textbook for the course. However, there are some reference books that are recommended:

- Bjork, T., 1998, Arbitrage Theory in Continuous Time, Oxford University Press
- Fabozzi, F.J., 2001, The Handbook of Fixed Income Securities, McGraw-Hill
- Hull, J., 2006, Options, Futures, and other Derivatives, Prentice Hall
- Musiela, M. and M. Rutkowski, 1998, Martingale Methods in Financial Modelling, Springer

1. The Term Structure of Interest Rates

- instantaneous interest rate
- the yield of a zero-coupon bond, spot rate
- forward interest rate
- term structure of spot rates
- term structure of discount factors
- term structure of forward rates

4. Instantaneous Forward Interest Rate Models

- the Heath-Jarrow-Morton framework
- the no-arbitrage condition of the HJM framework

5. LIBOR models

- spot LIBOR, forward LIBOR
- floating rate notes
- interest rate swaps, swap rate
- “bootstrapping” using swap rates
- interest rate options: caps, floors
- cap-floor-swap parity

6. The Term Structure of Defaultable Bonds

- structural models: Merton model with stochastic interest rates
- reduced form models

Course Materials