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SMA4241 Course Outline

The SMA4241 Financial Mathematics course at the National University of Science and Technology aims to provide an introduction to financial mathematics, requiring a background in probability and mathematical analysis. Key topics include financial markets, risk-free and risky assets, option pricing models, and hedging strategies, with assessments based on tests, assignments, and a final exam. Students must participate in an online classroom for resources and communication, and the course emphasizes model development for further research in the field.

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7 views2 pages

SMA4241 Course Outline

The SMA4241 Financial Mathematics course at the National University of Science and Technology aims to provide an introduction to financial mathematics, requiring a background in probability and mathematical analysis. Key topics include financial markets, risk-free and risky assets, option pricing models, and hedging strategies, with assessments based on tests, assignments, and a final exam. Students must participate in an online classroom for resources and communication, and the course emphasizes model development for further research in the field.

Uploaded by

zvingwaruthabani
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Course outline for SMA4241 Financial Mathematics

National University of Science and Technology


Faculty of Applied Sciences
Department of Applied Mathematics,
Lecturer : Mr T. Gwebu, Office Wf4
email: thabani.gwebu@nust.ac.zw
Class code 3kyh2h4
May 31, 2021

1 Summary
The aim of this course is to give a rigorous yet accessible introduction to the modern theory of financial
mathematics. The students should have a background in probability theory and mathematical analysis. As a
secondary objective the student is to be equipped with the logic used to develop models in financial mathematics
in order for them to pursue further research in the field. An online classroom is available where various resources,
assignments, worksheets, notifications and exercises will be made available on a regular basis. It is compulsory
to participate, as assignment submissions and communications with the lecturer will ONLY be accepted via this
platform. No other communication will be accepted. For more information on how you can access this online
classroom, please approach the lecturer. Note that your official NUST student email address which consists of
your student number, has to be functional for one to join this online classroom.

2 Topics
• FINANCIAL MARKETS AND INSTRUMENTS

– Introduction to financial mathematics.


– Basic definitions. Define a derivative contract, namely defining an option, future, forward and a
swap.
– The types of markets; that is, over the counter as opposed to the exchange market.
– The types of derivative traders; arbitrageurs, speculators and hedgers
– Model assumptions.
• RISK FREE ASSETS
– Simple interest
– Periodic compounding
– Continuous compounding
– Amortization
• RISKY ASSETS

– Dynamics of stock price


– Binomial tree 1 and 2 step model
– Continuous time stock model

1
– Martingales
• OPTIONS AND OPTION PRICING MODELS

– Portfolios and portfolio replication.


– European and American options in the binomial tree models.
– Other option pricing models.

• HEDGING OPTION POSITION

– Greek parameters

3 Assessment
The assessment in this course will be based on the following.
• Two tests.
• 1 programming assignment submitted online via the Google Classroom platform.

• 1 group assignment which will be presented in class.


• Assignments will be submitted online via the Google Classroom platform.(NB the number of assignments
will be guided by students co-operation during lectures )
• One 3 hour long examination to be written towards the end of the semester.

• The final examination contributes 75% to the overall course mark. The remaining 25% is derived from
the continuous assessment.

4 Textbooks
• Paul Wilmott Introduces Quantitative Finance, Paul Wilmott, Second Edition, John Wiley & Sons, Ltd,
2007.
• Options, Futures, and other Derivatives, John C. Hull, Eighth Edition, Pearsons, 2012.
• Notes on Stochastic Finance, Nicolas Privault, Available Online:
http://www.ntu.edu.sg/home/nprivault/index.html
• Stochastic Calculus for Finance I, The Binomial Asset Price Model, Steven E. Shreve, Springer-Verlag,
2004.

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