MATHS 4112 - Financial Modelling: Tools & Techniques - Honours

North Terrace Campus - Semester 2 - 2021

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
    Course Financial Modelling: Tools & Techniques - Honours
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1010 or MATHS 1011 or ECON 1010
    Assumed Knowledge Familiarity with Excel spreadsheets
    Restrictions Honours students only
    Course Description 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.
    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-arbitrageXX
    University Graduate Attributes

    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
    Career and leadership readiness
    • 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
    Required 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.
    Workload

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


    Activity

    Quantity

    Workload Hours

    Weekly online materials
    Tutorials
    In-tutorial tests
    Online quizzes
    Assignments
    12 weeks
    3 tutorials
    2 tests
    2 quizzes
    4 assignments
    100 hours
    12 hours
    2 hours
    2 hours
    40 hours
    Total 156 hours
    Learning Activities Summary
    Topics

    1. Call options - European and American
    2. Trading options
    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
    Exam 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 1
    Assignment 2
    Online quiz 1
    In-tute test 1
    Assignment 3
    Online quiz 2
    In-tute test 2
    Assignment 4
    Week 2
    Week 4
    Week 6
    Week 7
    Week 7
    Week 10
    Week 11
    Week 11
    Week 3
    Week 5
    Week 6
    Week 7
    Week 8
    Week 10
    Week 11
    Week 12
    6%
    6%
    8%
    15%
    6%
    8%
    15%
    6%
    Submission
    Assignments are to be submitted online via MyUni. Late assignments will not be accepted.
    Course Grading

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

    M11 (Honours Mark Scheme)
    GradeGrade reflects following criteria for allocation of gradeReported on Official Transcript
    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

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    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
  • Fraud Awareness

    Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.