Program

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Module Four

Interest Rates and Products

This module starts with a review of fixed income products and the simple but useful concepts of yield, duration and convexity, showing how they can be used in practice.

The limitations of this approach and the need for a more sophisticated theory are explained. Many of the ideas seen in the equity derivatives world are encountered again here but in a more complex form.

 

Fixed Income Products and Analysis

•    Names and properties of the basic and most important fixed-income products
•    Features commonly found in fixed-income products
•    Simple ways to analyze the market value of the instruments: yield, duration and convexity
•    How to construct yield curves and forward rates
•    Swaps
•    The relationship between swaps and zero-coupon bonds

 

Stochastic Interest Rate Modeling

•    Stochastic models for interest rates
•    How to derive the pricing equation for many fixed-income products
•    The structure of many popular one-factor interest rate models
•    The theoretical framework for multi-factor interest rate modeling
•    Popular two-factor models

 

Calibration and Data Analysis

•    How to choose time-dependent parameters in one-factor models so that
•    Today’s yield curve is an output of the model
•    The advantages and disadvantages of yield curve fitting
•    How to analyze short-term interest rates to determine the best model for the volatility and the real drift
•    How to analyze the slope of the yield curve to get information about the market price of risk

 

Heath Jarrow and Morton Model

•    The Heath, Jarrow & Morton (HJM) forward rate model
•    The relationship between HJM and spot rate models
•    The advantages and disadvantages of the HJM approach
•    How to decompose the random movements of the forward rate curve into its principal components

 

Probabilistic methods for interest rates

•    The pricing of interest rate products in a probabilistic setting
•    The equivalent martingale measures
•    The fundamental asset pricing formula for bonds
•    Application for popular interest rates models
•    The dynamics of bond prices
•    The forward measure
•    The fundamental asset pricing formula for derivatives on bonds

 

The Libor Market Model

•    The Libor Market model
•    The market view of the yield curve
•    Yield curve discretisation
•    Standard Libor market model dynamics
•    Numéraire and measure
•    The drift
•    Factor reduction

 

Cointegration: Modeling Long Term Relationships

•    Multi-variate time series model: An introduction to VectorAutoregressiion
•    Stationarity and Unit Root Test
•    Cointegrating relationship
•    An introduction to Vector Error Correction Model
•    Reduced rank regression technique: an introduction to Johansen ML Procedure