Module MATH3301: Mathematical Finance III

Department: Mathematical Sciences

MATH3301: Mathematical Finance III

Type	Level	Credits	Availability	Module Cap	Location
Open	3	20	Available in 2026/2027		Durham

Pre-requisites

Probability II (MATH2647) OR Probability II (MATH2751)

Corequisites

One 20 credit Level 3 mathematics module.

Excluded Combinations

Aims

To provide an introduction to the mathematical modelling of financial derivative products.

Content

An introduction to options and markets.
Asset price random walks.
The Black-Scholes model and the Black-Scholes pricing formula.
Brownian motion.
Stochastic calculus: Itô processes and Itô's formula.
Self-financing, replicating portfolios and martingale measures.
Risk-neutral valuation.

Learning Outcomes

Subject-specific Knowledge

By the end of the module students will be able to:
Demonstrate an understanding of the mathematics of pricing in basic financial markets in discrete and continuous time, based on fundamental principles of no-arbitrage, risk-neutral measures, and replicating portfolios.
Use the underlying probabilistic models to solve relevant financial problems; work with probability and change-of-measure computations; prove and apply pricing theorems in the context of binomial-tree markets and Black-Scholes markets.
Apply the theory of Brownian motion and stochastic calculus; derive properties of continuous-time stochastic processes; work with Ito’s lemma and Girsanov’s theorem.

Subject-specific Skills

Students will have enhanced mathematical skills in the following areas: modelling, computation. Moreover, students will have developed an appreciation of, and ability in, mathematical modelling in the financial world.

Key Skills

Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total Hours	Attendance Monitored
Lectures	40	2 per week in Michaelmas and Epiphany	1 Hour	40
Problem Classes	10	Fortnightly in Michaelmas and Epiphany; 2 in Easter	1 Hour	10	Yes
Preparation and Reading				150
Total				200

Summative Assessment

Component	Component Weighting	Element	Length/Duration	Element Weighting	Resit Opportunity
Examination	70%	On Campus Written Examination	2 hours	100%
Summative Assignments	30%	Assignment	4 assignments	100%

Formative Assessment

Four assignments to be submitted.

Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.