UCL School of Management

# MSIN0108: Fixed Income Modelling

Taught by
Level
Masters, level 7
Prerequisites
None
Eligibility
MSc Finance students only
Terms
2
Delivery method
3-hour lecture (x 5 weeks). The module will take place in the first five weeks of term two.
Assessment
Exam 80%
Group Coursework 20%
Previous Module Code
MSING069

#### Course overview

This is an optional module introducing aspects of the fixed-income world in a financial engineering setting. The underlying of concern is primarily the spot interest-rate. Students wishing develop a quantitative finance basis for their MSc study will find this elective particularly beneficial. The theme of the course is to build the mathematical framework for pricing interest-rate securities. Derivation of important models and equations will be presented. The numerical and computational schemes for contract valuation will centre on the Monte-Carlo scheme.

#### Learning outcomes

• Understand the basic products traded in the fixed income markets
• Develop knowledge of mathematical models, their derivation and solution methods
• Be able to price more complex products computationally
• Understand what happens inside the ‘black-box’ rather than simply place blind faith in given mathematical formulae.

#### Topics covered

Fixed-Income products and markets: A brief overview of the fixed-income markets and the securities traded in them – zero coupon bonds and coupon bearing bonds; yield curves and forward rates; duration and convexity. Caps, Floors, Swaps.

Mathematical review: Stochastic Differential Equations for interest-rate models; drift, volatility and mean reversion. Itô’s lemma.

Stochastic interest rate models: Popular spot-rate models (Vasicek, Cox-Ingersoll-Ross). Bond pricing equation and similarities with the Black-Scholes equation; Market price of interest-rate risk and why it arises. Risk-neutral pricing. Tractable models and Affine solutions of the bond pricing equation. The need for multi-factor interest rate modelling: two-factor interest rate models (Brennan & Schwartz; Fong & Vasicek; Longstaff & Schwartz); and bond pricing equation. Stochastic market price of risk.

Calibration: Yield curve fitting – the importance of matching theoretical and market bond prices; time dependent one factor models (Ho & Lee, Hull & White).

Heath, Jarrow and Morton (HJM): HJM model and evolution of the whole yield curve. Monte-Carlo simulations and implementing HJM. Computations in Excel.

Market Models: Dynamics of discrete forward rates – Libor Market Model. Brace, Gatarek, Musiela (BGM) model.

#### Assessment summary

Exam 80% Group Coursework 20%

Current students should refer to Moodle for specific details of the current year’s assessment.