Module: Fixed Income Securities (Advanced)

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Fixed Income Securities (Advanced)
Module Code	MTH1071 (ITS: MS525)
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	9	Credit Rating	7.5

Description

This graduate course focuses on a rigorous treatment of models for pricing and hedging fixed-income securities, with emphasis on continuous-time. Interest-rate contracts: bonds, swaps, caps and floors, options, swaptions. Term-structure estimation: bootstrap, splines. Shortrate models: Vasicek, Cox-Ingersoll-Ross, and related models. Forward-rates and Heath-Jarrow-Morton approach. Market (LIBOR) models.

Learning Outcomes

1. 1DBC9D68-0B30-0001-34D0-16B31200B870
2. Price fixed-income securities
3. 1DBC9D68-11C7-0001-A43C-18A44EB01B87
4. Estimate the term structure
5. 1DBC9D68-333C-0001-BB75-15F01300EFF0
6. Prove main results in fixed-income theory
7. 1DBCA491-400B-0001-D88E-1A1E196B1953
8. Design strategies to hedge and immunize liabilities linked to interest-rates
9. 1DBCA491-76B0-0001-B115-16D015D11CDC
10. Evaluate critically relative advantages of various model specifications
11. 1DBCA491-8E73-0001-BC78-195D1C60F220
12. Develop pricing and hedging methods for new interest-rate related products

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	Classes
Directed learning	3	Final Exam
Seminars	5	Attendance to Research Seminars
Independent Study	150	Independent work on textbooks and related papers
Total Workload: 194

Section Breakdown
CRN	20798	Part of Term	Semester 2
Coursework	0%	Examination Weight	100%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Paolo Guasoni	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Formal Examination	End-of-Semester Final Examination	100%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Interest Rates and Related Contracts
Zero-Coupon Bonds, Interest Rates, Money-Market Account and Short Rates, Coupon Bonds, Swaps and Yields, Market Conventions, Caps and Floors, Swaptions

Estimating the Term-Structure
Bootstrapping, Non-parametric Estimation Methods, Parametric Estimation Methods, Principal Component Analysis

Short-Rate Models
Diffusion Short-Rate Models, Inverting the Forward Curve, Affine Term-Structures, Vasicek Model, CIR, Dothan Model, Ho–Lee Model, Hull–White Model

Heath–Jarrow–Morton (HJM) Methodology
Forward Curve Movements, Absence of Arbitrage, Short-Rate Dynamics, HJM Models, Proportional Volatility, Fubini’s Theorem

Forward Measures
T -Bond as Numeraire, Bond Option Pricing, Black–Scholes Model with Gaussian Interest Rates

Forwards and Futures
Forward Contracts, Futures Contracts, Interest Rate Futures, Forward vs. Futures in a Gaussian Setup

Market Models
Heuristic Derivation, LIBOR Market Model, LIBOR Dynamics Under Different Measures, Implied Bond Market, Implied Money-Market Account, Swaption Pricing, Monte Carlo Simulation of the LIBOR Market Model, Volatility Structure and Calibration, Continuous-Tenor Case

Indicative Reading List

Books:

Damir Filipovic,: 0, Term-Structure Models: A Graduate Course, 978-3-540-09726-6
Pietro Veronesi: 2010, Fixed income securities, Wiley, Hoboken, N.J., 0470109106

Articles:
None

Other Resources

None