Undergraduate Course: Financial Mathematics (MATH10003)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
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 noone 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 noarbitrage.
(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); Noarbitrage pricing theory via risk neutral probabilities and via portfolio strategies.
(D) Introduction to stochastic analysis: Brownian motion, Ito integral, Ito Formula, stochastic differential equations; BlackScholes model and Option pricing within BlackScholes model. BlackScholes 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.

Information for Visiting Students
Prerequisites  Visiting 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 Mathematics  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Demonstrate knowledge of basic financial concepts and financial derivative instruments.
 Fundamentally understand the noArbitrage pricing concept.
 Apply basic probability theory to option pricing in discrete time in the context of simple financial models.
 Demonstrate fundamental knowledge of stochastic analysis (Ito Formula and Ito Integration) and the BlackScholes formula.
 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. SpringerVerlags 2004
Shreve, Steven E.. Stochastic calculus for finance. II. SpringerVerlag 2004

Contacts
Course organiser  Dr Chak Hei Lo
Tel: (0131 6)50 5387
Email: C.Lo@ed.ac.uk 
Course secretary  Mr Christopher Palmer
Tel: (0131 6)50 5060
Email: chris.palmer@ed.ac.uk 

