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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Financial Mathematics (MATH10003)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
Summary"Optional course for Honours Degrees involving Mathematics and/or Statistics; stipulated course for Honours in Economics and Statistics.

This course is a basic introduction to finance. It starts by making an introduction to the value of money, interest rates and financial contracts, in particular, what are fair prices for contracts and why no-one uses fair prices in real life. Then, there is a review of probability theory followed by an introduction to financial markets in discrete time. In discrete time, one will see how the ideas of fair pricing apply to price contracts commonly found in stock exchanges. The next block focuses on continuous time finance and contains an introduction to the basic ideas of Stochastic calculus. The last chapter is an overview of Actuarial Finance. This course is a great introduction to finance theory and its purpose is to give students a broad perspective on the topic."
Course description Syllabus summary:

(A) Introduction to financial markets and financial contracts; value of money; basic investment strategies and fundamental concepts of no-arbitrage.

(B) Basic revision of probability theory (random variables, expectation, variance, covariance, correlation; Binomial distribution, normal distribution; Central limit theorem and transformation of distributions).

(C) The binomial tree market model; valuation of contracts (European and American); No-arbitrage pricing theory via risk neutral probabilities and via portfolio strategies.

(D) Introduction to stochastic analysis: Brownian motion, Ito integral, Ito Formula, stochastic differential equations; Black-Scholes model and Option pricing within Black-Scholes model. Black-Scholes PDE

(E) Time value of money, compound interest rates and present value of future payments. Interest income. The equation of value. Annuities. The general loan schedule. Net present values. Comparison of investment projects.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND ( Probability (MATH08066) OR Probability with Applications (MATH08067))
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Academic year 2020/21, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 6, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 68 )
Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 5%, Examination 95%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Financial Mathematics2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate knowledge of basic financial concepts and financial derivative instruments.
  2. Fundamentally understand the no-Arbitrage pricing concept.
  3. Apply basic probability theory to option pricing in discrete time in the context of simple financial models.
  4. Demonstrate fundamental knowledge of stochastic analysis (Ito Formula and Ito Integration) and the Black-Scholes formula.
  5. Understand the introduction to actuarial mathematics.
Reading List
Björk, Tomas. Arbitrage theory in continuous time. 3rd Edition, Oxford Uni-
versity Press 2009

Hull, John C. Options, Futures and Other Derivatives. Elsevier/Butterworth
Heinemann, 2013

Shreve, Steven E.. Stochastic calculus for finance. I. Springer-Verlags 2004

Shreve, Steven E.. Stochastic calculus for finance. II. Springer-Verlag 2004
Additional Information
Course URL
Graduate Attributes and Skills Not entered
Course organiserDr Chak Hei Lo
Tel: (0131 6)50 5387
Course secretaryMr Christopher Palmer
Tel: (0131 6)50 5060
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