Module Code - Title:
MS4027
-
FUNDAMENTALS OF FINANCIAL MATHEMATICS
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
MS4035
Rationale and Purpose of the Module:
This course is an introduction to financial mathematics.
Using discrete-time stochastic models, the pricing and hedging
of financial derivatives in arbitrage-free markets is studied.
Syllabus:
Introduction to Derivative Securities: Futures, Forwards, European,
path-dependent, and American stock options.
Introduction to Interest Rate Derivatives,
with a focus on bonds and Forward Rate Agreements.
Using arbitrage arguments to prove properties of options, inequalities, as well as the put-call parity. Introduction to binomial trees and risk-neutral
valuation of options via replication arguments (delta-hedging).
Probability theory on finite sample spaces: conditional expectations, martingales,
risk-neutral pricing. Use the concept of conditional expectation
to formulate and prove the Fundamental Theorems of Asset Pricing I and II.
Value and super-replication of American put options.
Simple time-series models (ARMA(p,q)) for modelling and trading trends
and mean-reversion.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
1. Define the basic derivative securities and better-known exotic options.
2. Use arbitrage as a pricing tool.
3. Understand the mechanics of basic interest rate products such as bonds,
forward rate agreements and swaps.
4. Apply discrete probability theory to pricing and hedging
of path-dependent claims in complete markets.
5. Evaluate (``back-test'') trading strategies using historical time series
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
The module will have the usual lecture/tutorial format.
A Case Study will be assigned which will be part of the overall grade.
Students' participation in tutorials is expected,
where solutions to weekly problems are presented.
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Hull, J.C. (2006)
Options, Futures and other Derivative Securities (6ed)
, Pearson
Shreve, S.E. (2005)
Stochastic Calculus for Finance I
, Springer
Other Relevant Texts:
Programme(s) in which this Module is Offered:
MSMAMOTFA - MATHEMATICAL MODELLING
Semester(s) Module is Offered:
Autumn
Module Leader:
eberhard.mayerhofer@ul.ie