# STATS 370 : Financial Mathematics

## Science

### Course Prescription

Mean-variance portfolio theory; options, arbitrage and put-call relationships; introduction of binomial and Black-Scholes option pricing models; compound interest, annuities, capital redemption policies, valuation of securities, sinking funds; varying rates of interest, taxation; duration and immunisation; introduction to life annuities and life insurance mathematics.

### Course Overview

Students should enrol in this course to gain exposure to the essential mathematical ideas of Finance. Practical examples of dealing with securities, portfolios, and options are central to this course, which lies at the intersection between Statistics, Mathematics, and Finance. While no financial background is necessary, students are required to have passed at least 15 points at Stage II in Mathematics and 15 points at Stage II in Statistics. Think like a Wall Street whizz!

### Course Requirements

Prerequisite: 15 points at Stage II in Mathematics and 15 points at Stage II in Statistics Restriction: STATS 722

### Capabilities Developed in this Course

 Capability 3: Knowledge and Practice Capability 4: Critical Thinking Capability 5: Solution Seeking Capability 6: Communication

### Learning Outcomes

By the end of this course, students will be able to:
1. Demonstrate the techniques used to model financial securities prices (Capability 3, 5 and 6)
2. Perform calculations yielding valuation and hedging strategies for standard financial options (Capability 3, 4 and 5)
3. Distinguish between factors affecting the value of financial derivatives (Capability 3, 4 and 6)
4. Analyse the structure of optimal investment portfolios with specified levels of return and risk (Capability 3, 5 and 6)
5. Perform analysis of investment portfolio efficiency and structure (Capability 3, 4 and 6)
6. Perform calculations of interest payments and schedules (Capability 3 and 6)

### Assessments

Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Test 20% Individual Test
Final Exam 50% Individual Examination
1 2 3 4 5 6
Assignments
Test
Final Exam

Must obtain at least 50% in final exam to pass the course.

### Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

### Key Topics

• Part 1 (Stochastic securities valuation, 6 weeks). Random variables, distributions and expected values, introduction to derivative securities, stocks, forward contracts, European call and put options, arbitrage, the binomial model for stock prices, risk-neutral valuation, Brownian motion, geometric Brownian motion model of the stock price process, put-call relationships, Black-Scholes analysis and pricing formulae, American options, the Greeks.
• Part 2 (Mean-Variance Portfolio Theory, 4 weeks). Investments, portfolios, returns, mean, variance and covariance of returns, minimum variance portfolio for two investments, portfolio possibilities curves and their properties, more than two assets, diversification, portfolio possibilities regions and their properties, efficient portfolio frontier, riskless lending and borrowing, short sales, computing the efficient frontier, single index structural models.
• Part 3 (Interest, 2 weeks). Simple and compound interest, effective and nominal interest rates, accumulation factors, force of interest, equivalent interest rates, present values (of cashflows) interest income, basic compound interest functions, equation of value for a sequence of transactions, yield, annuities, and loan schedules.

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, a typical weekly workload includes:

• 3 hours of lectures
• A 1-hour lab
• 3 hours of reviewing the course content
• 3 hours of work on assignments and/or test preparation

### Delivery Mode

#### Campus Experience

Lectures will be available as recordings.

### Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

Lecture notes will be made available on Canvas.

The textbook "Statistics and Finance: An Introduction" by David Ruppert is suggested as recommended reading, but not required.

### Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

Some students now have limited experience with R. The use of R in assignments will be limited accordingly.

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

### Class Representatives

The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

### Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

### Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page .

This should be done as soon as possible and no later than seven days after the affected test or exam date.

### Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

### Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter .

### Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:54 a.m.