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: Fixed and floating rates, bonds, swaps, caps and floors.
• Yield, duration and convexity: Definitions, use and limitations, bootstrapping to build up the yield curve from bonds and swaps.
• Stochastic interest rate models, one and two factors: Transferring ideas from the equity world, differences from the equity world, popular models, data analysis.
• Data analysis: Choosing the best model
• Calibration: Fitting the yield curve in simple models, use and abuse.
• Convertible bonds: Conversion, callability, putability, random factors.
• Heath, Jarrow and Morton model: Modelling the yield curve.

Lecture 4.1

• 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

Lecture 4.2

• 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

Lecture 4.3

• 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

Lecture 4.4

• The basic Convertible Bond (CB)
• Market conventions for the pricing and analysis of CBs
• Converts as options
• CB arbitrage
• Pricing convertibles

Lecture 4.5

• Heath, Jarrow and Morton model
• Evolution of the entire yield curve
• Risk neutrality

Preparatory reading:

• P. Wilmott, Paul Wilmott Introduces Quantitative Finance, 2001, John Wiley. Chapters 14—19
• M. Jackson and M. Staunton, Advanced Modelling in Finance Using Excel and VBA, 2001, John Wiley.
  Chapters 14—16
• E.G. Haug, The Complete Guide to Option Pricing Formulas, second edition, 2007, McGraw-Hill Professional.
  Chapters 11, 14
• P. Wilmott, Paul Wilmott On Quantitative Finance, second edition, 2006, John Wiley. Chapters 31-33, 36, 37

Further reading:

• N. Taleb, Dynamic Hedging, 1996, John Wiley
• J.C. Hull, Options, Futures and Other Derivatives (5th Edition), 2002, Prentice-Hall

Follow-up recording(s), extra lecture(s):

• CB Coding Workshop
• Term Sheets