# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2023/2024

### Timetable information in the Course Catalogue may be subject to change.

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# Undergraduate Course: Financial Mathematics (MATH10003)

 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 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. 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.
 Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND Probability (MATH08066) Co-requisites Prohibited Combinations Other requirements Students can have passed Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND Probability with Applications (MATH08067)
 Pre-requisites 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
 Academic year 2023/24, 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
 On completion of this course, the student will be able to: Demonstrate knowledge of basic financial concepts and financial derivative instruments.Fundamentally understand the no-Arbitrage 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 Black-Scholes formula.Understand the introduction to actuarial mathematics.
 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
 Course URL https://info.maths.ed.ac.uk/teaching.html Graduate Attributes and Skills Not entered Keywords FiM
 Course organiser Dr Jiawei Li Tel: (0131 6)50 5043 Email: jiawei.li@ed.ac.uk Course secretary Miss Greta Mazelyte Tel: Email: greta.mazelyte@ed.ac.uk
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