Type of Credit: Elective
Credit(s)
Number of Students
The purpose of this course is to explore the bond markets and provide an introduction to the analysis of fixed income securities and derivatives from the perspective of financial mathematics in the theory of bond pricing and derivatives with a new level of complexity. The course is aimed at those students who would like to learn bond pricing and bond-derivative pricings under the continuous-time framework.
能力項目說明
Knowledge of continuous-time stochastic processes are required for this course, e.g., mathematical techniques as those covered in Chapter 14 of Hull (2022).
Students will understand what the risk-neutral valuation principle is for pricing interest rate derivatives/bond derivatives and learn the more general martingale pricing method after taking this course.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
Topic 1 - Arbitrage-Free Pricing: Fundamental Theorem of Asset Pricing
Topic 2 - Discrete-Time Binomial Models
Topic 3 - Continuous-Time Interest Rate Models - General
One-Factor Models for the Risk-Free Rate
The Martingale Approach
The PDE Approach to Pricing
Topic 4 - Continuous-Time Interest Rate Models
The Vasicek Model
The Cox-Ingersoll-Ross Model
Affine Short-Rate Models
Other Short-Rate Models
Topic 5 No-Arbitrage Models5.1 Introduction 85
Markov Models
The Heath-Jarrow-Morton (HJM) Framework
Topic 6 - The Forward-Measure Approach
A New Numeraire
Change of Measure
A Replicating Strategy
Topic 7 - Market Models
Market Rates of Interest
LIBOR Market Models: the BGM Approach
Simulation of LIBOR Market Models
Swap Market Models
Grades in this course will be based on homework assignments (including a term paper) and class participation.
The class participation is based on the students’ ability to initiate and participate in discussions as well as all materials covered during class.
The term paper for the course is a written report on the analysis of a selected interest rate derivatives.
Supplementary readings related to specific topics covered in the class will be assigned for either class discussion/presentation or homework.
Cairns, Andrew J. G., Interest Rate Models: An Introduction, Princeton University Press, 2004.
Fabozzi, F., Bond Markets, Analysis and Strategies, Prentice-Hall: Englewood Cliffs, New Jersey, 8th edition, 2012.
Some journal articles and research papers will be assigned as supplementary and additional materials during the semester