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  Ciprian Necula - Interest Rate Derivatives - Fall 2014
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Instructor: Ciprian NECULA

Course Description

This course is part of the Risk Management module and 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.

Prerequisites

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

Grading

30% project, 70% final exam (open book)

Textbooks

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

Tentative Course Outline

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

2. Instantaneous Interest Rate Models

- the fundamental valuation equation of a zero-coupon bond, the market price of risk
- affine term structure models
- Vasicek model, CIR model
- calibration to data: Hoo-Lee model, Hull-White model
- forwads on zero-coupon bonds
- options on zero-coupon bonds
- futures on zero-coupon bonds

3. Coupon-bearing Bonds

- clean price, dirty price, accrued interest, yield
- “bootstrapping” using coupon-bearing bonds
- forwads on coupon-bearing bonds
- options on coupon-bearing bonds
- futures on coupon-bearing bonds
- sensitivity indicators of a bond portfolio: PVBP, duration, convexity
- hedging a bond portfolio using futures contracts

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

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