## MATHS 4112 - Financial Modelling: Tools & Techniques - Honours

### North Terrace Campus - Semester 2 - 2016

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 4112 Financial Modelling: Tools & Techniques - Honours Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 3 hours per week MATHS 1010 or MATHS 1011 APP MTH 3011, APP MTH 3012 Familiarity with Excel spreadsheets Ongoing Assessment 30%, Exam 70%
##### Course Staff

Course Coordinator: Adjunct Professor David Clements

##### 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-arbitrageXX

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
• Learning & Teaching Activities
##### Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and sample problems. A sequence of of written assignments provides the assessment opportunities for students to gauge their progress and understanding.

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

 Activity Quantity Workload Hours LecturesTutorialsAssignments 3055 901848 Total 156
##### Learning Activities Summary
Lecture Outline

1. Call options - European
2. Call options - American
3. Binomial assett pricing model
4. Price derivatives using risk neutral probabilities
5. Forward contracts
6. Multipstep binomial models (2 lectures)
7 Arrow-Debreu securities and state prices (2 lectures)
8. Cox-Ross-Rubibstein (CRR) convergence, Black Scholes formula (2 lectures)
9. Calculations with the Black-Scholes formula (2 lectures)
10. Generalise multistep models
11. Pricing American options with CRR multistep model
12. Barrier options
13. Forward commodity contracts
14. Forward currency contracts (2 lectures)
15. Interest rate derivatives (2 lectures)
16. Ho and Lee model for interest rates (2 lectures)
17. Futures markets (2 lectures)
18. Hedging and contingent claims (2 lectures)
19. Sensitivity of options (2 lectures)
20. Options with dividend paying assets
21. Review lecture

Tutorial Outline
1. Call options, one-step binomial pricing model
2. CRR model
3. Three-step CRR model and Arrow-Debreu prices
4. Pricing American options in a two-step CRR model
5. The ‘Greeks’ and delta hedging

Assignment Outline
1. One-step binomial model
2. Two-step CRR model, Black-Scholes model
3. Pricing American options using the CRR model
4. Forward and futures contracts
5. Delta hedging, Ho-Lee model
• 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 30% all Exam 70% 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 2Assignment 3Assignment 4Assignment 5 Week 2Week 4Week 6Week 8Week 10 Week 3Week 5Week 7Week 9Week 11 6%6%6%6%6%
##### Submission
1. All written assignments are to be submitted to the designated hand-in boxes. within the School of Mathematical Sciences with a signed cover sheet attached.

2. Late assignments will not be accepted.

3. Assignments will have a two week turn-around time for feedback to students.

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

M11 (Honours Mark Scheme)
Fail A mark between 1-49 F
Third Class A mark between 50-59 3
Second Class Div B A mark between 60-69 2B
Second Class Div A A mark between 70-79 2A
First Class A mark between 80-100 1
Result Pending An interim result RP
Continuing Continuing CN

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.

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• Policies & Guidelines
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