## MATHS 3012 - Financial Modelling: Tools & Techniques III

### North Terrace Campus - Semester 2 - 2020

The growth of the range of financial products that are traded on financial markets or are available at other financial institutions, is a notable feature of the finance industry. A major factor contributing to this growth has been the development of sophisticated methods to price these products. The significance to the finance industry of developing a method for pricing options (financial derivatives) was recognized by the awarding of the Nobel Prize in Economics to Myron Scholes and Robert Merton in 1997. The mathematics upon which their method is built is stochastic calculus in continuous time. Binomial lattice type models provide another approach for pricing options. These models are formulated in discrete time and the examination of their structure and application in various financial settings takes place in a mathematical context that is less technically demanding than when time is continuous. This course discusses the binomial framework, shows how discrete-time models currently used in the financial industry are formulated within this framework and uses the models to compute prices and construct hedges to manage financial risk. Spreadsheets are used to facilitate computations where appropriate. Topics covered are: The no-arbitrage assumption for financial markets; no-arbitrage inequalities; formulation of the one-step binomial model; basic pricing formula; the Cox-Ross-Rubinstein (CRR) model; application to European style options, exchange rates and interest rates; formulation of the n-step binomial model; backward induction formula; forward induction formula; n-step CRR model; relationship to Black-Scholes; forward and future contracts; exotic options; path dependent options; implied volatility trees; implied binomial trees; interest rate models; hedging; real options; implementing the models using EXCEL spreadsheets.

• General Course Information
##### Course Details
Course Code MATHS 3012 Financial Modelling: Tools & Techniques III Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 3 hours per week Y MATHS 1010 or MATHS 1011 or ECON 1010 Familiarity with Excel spreadsheets Ongoing Assessment, Exam
##### Course Staff

Course Coordinator: Professor Joshua Ross

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
On successful completion of this course students will be able to:
1. demonstrate an understanding of basic financial market concepts
2. construct binomial tree models
3. price a wide variety of contingent claims using principles of non-arbitrage

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Deep discipline knowledge
• informed and infused by cutting edge research, scaffolded throughout their program of studies
• acquired from personal interaction with research active educators, from year 1
• accredited or validated against national or international standards (for relevant programs)
1,2,3
Critical thinking and problem solving
• steeped in research methods and rigor
• based on empirical evidence and the scientific approach to knowledge development
• demonstrated through appropriate and relevant assessment
1,2,3
Teamwork and communication skills
• developed from, with, and via the SGDE
• honed through assessment and practice throughout the program of studies
• encouraged and valued in all aspects of learning
2,3
• technology savvy
• professional and, where relevant, fully accredited
• forward thinking and well informed
• tested and validated by work based experiences
1,2,3
• Learning Resources
None.
##### Recommended Resources
1. Binomial Models in Finance by J Van Der Hoek and R Elliot, Cambridge
2. Elementary Calculus of Financial Mathematics by Roberts, Cambridge
3. Options, Futures, and Other Derivatives 7th ed. by Hull, Pearson
##### Online Learning
This course uses MyUni exclusively for providing electronic resources, such as notes, videos, quizzes, assignments and solutions et cetera.
• Learning & Teaching Activities
##### Learning & Teaching Modes
Each week, lecture notes will be provided, designed to be read in advance of viewing videos. Videos will consist of the lecturer explaining key material and examples from the lecture notes. Tutorials supplement this, providing exercises to enhance learning and confirm understanding including interaction with the lecturer and/or tutor. Four written assignments, two online quizzes and two in-tute tests during semester provide the assessment opportunities for students to gauge and demonstrate their progress and understanding. Regular consulting sessions can be used to interact with the lecturer and/or tutor for additional tution.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload Hours Weekly online materialsTutorialsIn-tutorial testsOnline quizzesAssignments 12 weeks3 tutorials2 tests2 quizzes4 assignments 100 hours12 hours2 hours2 hours40 hours Total 156 hours
##### Learning Activities Summary
Topics

1. Call options - European and American
3. Put options
4. Arbitrage
5. Binomial assett pricing model
6. Price derivatives using risk neutral probabilities
7. Cox-Ross-Rubinstein (CRR) model
8 Arrow-Debreu securities and state prices
9. Black Scholes model
10. Volatility
11. Variable interest rates
12. Valuing American options
13. Barrier options
14. Forward contracts
15. Interest rate derivatives
16. Bonds
17. Ho-Lee model
18. Futures markets
19. Managing risk
20. Hedging
21. Sensitivity of options

Tutorial Outline

1. Call options and the CRR model
2. Multi-step models and Arrow-Debreu securities
3. Valuing American options

• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Component Weighting Objective Assessed Assignments 24% all Online quizzes 16% all In-tute tests 30% all Examination 30% all
##### Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.

##### Assessment Detail
 Assessment Item Distributed Due Date Weighting Assignment 1Assignment 2Online quiz 1In-tute test 1Assignment 3Online quiz 2In-tute test 2Assignment 4 Week 2Week 4Week 6Week 7Week 7Week 10Week 11Week 11 Week 3Week 5Week 6Week 7Week 8Week 10Week 11Week 12 6%6%8%15%6%8%15%6%
##### Submission
Assignments are to be submitted online via MyUni. Late assignments will not be accepted.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

• Student Feedback

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SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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