# Course syllabus - Introduction to Financial Mathematics 7.5 credits

### Introduktion till finansiell matematik

 Course code: MAA303 Valid from: Autumn semester13 Autumn semester19 Level of education: First cycle Subject: Mathematics Main Field(s) of Study: Mathematics/Applied Mathematics, Economics, In-Depth Level: G1F (First cycle, has less than 60 credits in first-cycle course/s as entry requirements), G1F (First cycle, has less than 60 credits in first-cycle course/s as entry requirements), School: UKK Ratification date: 2013-02-01

## Objectives

The aim of this course is to provide an understanding of financial instruments with a focus on financial derivatives and give knowledge in evaluating and pricing of the most common financial derivatives like forwards, futures and options.

## Learning outcomes

At the end of the course the student is expected to be able to
- describe the notions of forward contracts, futures contracts, options, interest rates, bonds and explain the arbitrage relations.
- evaluate forwards and futures and calculate bounds on options using simple arbitrage relations.
- build the Binomial model for asset prices and apply this model for European and American option pricing.
- perform arbitrage-pricing and perform risk-neutral valuation for options.
- explain the basic idea of the Black-Scholes model and use Black-Scholes formula to price.

## Course content

Introduction to derivative securities. Interest rates and bonds. Present value and future value. European and American options. Simple arbitrage relations for forwards, futures and options. Elementary discrete probability theory. Asset price dynamics. Multi-period Binomial pricing model. Pricing contracts via no-arbitrage principle. Risk-neutral valuation. Normal distribution. Geometrical Brownian motion and modeling asset price processes. Black-Scholes model and Black-Scholes option pricing formula.

## Teaching methods

Lectures, problem solving classes and seminars.

## Specific entry requirements

Either 7,5 credits in economics or Financial Accounting I 7,5 credits or equivalent. Also required are Calculus I 7,5 credits or equivalent and a TOEFL test result, minimum score 173 (CBT), 500 (PBT) or 61 (iBT) or an IELTS test result with an overall band score of minimum 5,0 and no band score below 4,5. The English test is COMPULSORY for all applicants except citizens of Australia, Canada, Ireland, New Zealand, United Kingdom and USA.

## Examination

Continuous examination and quizzes (PRO1), 3 credits, marks Pass (G)
Seminars (SEM1), 1.5 credits, marks Pass (G)
Written examination (TEN1), 3 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDH regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2016/0601). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

## Enviromental aspects

The course does not contain any specific environmental considerations.

Course literature is preliminary until 3 weeks before the course starts. Literature may be valid over several terms.

Valid from: Autumn semester13

Decision date: 2013-07-18

Last update: 2013-07-18

## Books

Options, futures, and other derivatives

ISBN: 978-0-273-75907-2 (pbk) LIBRIS-ID: 12308484

xxi, 847 s.

7 ed is ok as well.

## Reference Literature

An elementary introduction to mathematical finance : options and other topics

ISBN: 0-521-81429-4 (inb.) LIBRIS-ID: 8679325

xv, 253 s.

## Other Materials

Additional lecture notes will be used in the course.