Module: Fixed Income Securities (Advanced)

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Fixed Income Securities (Advanced)
Module Code	MS525 (ITS) / MTH1071 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Paolo Guasoni
Module Teachers	-
NFQ level	9	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None

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. Price fixed-income securities
2. Estimate the term structure
3. Prove main results in fixed-income theory
4. Design strategies to hedge and immunize liabilities linked to interest-rates
5. Evaluate critically relative advantages of various model specifications
6. 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

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

Assessment Breakdown
Continuous Assessment	0%	Examination Weight	100%

Type	Description	% of total	Assessment Date
Course Work Breakdown

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

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

Other Resources

None