Topic outline

  • General

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    This module introduces you to some of the most important financial instruments, including bonds, shares and derivatives (such as forward contracts and options). By using the assumption that arbitrage opportunities do not exist in the market, we show how it is possible to derive formulas for the fair prices of many types of derivatives. Some results can actually be derived in a model-independent way, although more generally we will work within the framework of a discrete-time trading model.

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      General Module Announcements Forum
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      Student Forum
      Forum Description: This forum is available for everyone to post messages to. Students can raise questions or discuss issues related to the module. Students are encouraged to post to this forum and it will be checked regulary by the module leader. Students should feel free to reply to other students if they are able to.
    • File icon
      General Module information File
      75.9 KB
    • File icon
      Complete Lecture Notes File
      586.7 KB
    • Quiz icon
      Semester A final assessment Quiz

      This assessment is intended to be completed within 3 hours. Although you are expected to finish the assessment within this time frame, you will be given an additional 30 minutes for scanning and submitting your handwritten solution in case you have not already done so.

      IMPORTANT – If you run out of time during this assessment, we will not accept IT issues as an extenuating circumstance. This is because we have given you ample time to complete and submit your work. If your attempt is still in progress at the end of the set time slot, any file you have uploaded will be automatically submitted.

      Please complete the assessment on a desktop or laptop. QMplus assessments are meant to be taken on these devices to prevent any issues viewing the questions and uploading answers. Please do not use your phone for this.

      • You may use books and notes. 

      • You may use calculators and computers, but you must show your working for any calculations you do. 

      • You may use the Internet as a resource, but not to ask for the solution to an exam question or to copy any solution you find. 

      • You must not seek or obtain help from anyone else.

  • Week 1: Topic title

    • week 1 - LECTURE

      • Interest rates and Present Value Analysis I

       

      week 1 - TUTORIAL


      • Please note that tutorials start next week, there is no tutorial this week (on Friday 29 Sept). Still you should already this week go over Coursework problems covered in this week's lecture, please do this on your own so that we can discuss your questions next week. 


      week 1 TASKS

      • Read the typed notes on this week's lecture (roughly Sections 1.1, 1.2, and 1.3). 
      • Read the probability review notes if you are unprepared in that area. 


    • File icon
      Review of Probability Theory File
      281.7 KB

      This document contains a brief review of the probability theory that is needed

      for this module. Most of it should be familiar. Please refer to this document

      if you are not comfortable with any of the probability theory that appears in lectures/coursework.


    • File icon
      Coursework 1 File
      139.8 KB

      Due date: Friday 6 October.


    • File icon
      Solutions to Coursework 1 File
      178.2 KB

  • Week 2: Topic title

    • week 2 - LECTURE

      • Interest rates and present value analysis II

       

      week 2 - TUTORIAL

       

      week 2 TASKS

      •  Read the typed notes of this week's lectures (roughly Sections 1.4 and 1.5).
      • Complete coursework 1.


  • Week 3: Topic title

  • Module Description

    • This module introduces you to some of the most important financial instruments, including bonds, shares and derivatives (such as forward contracts and options). By using the assumption that arbitrage opportunities do not exist in the market, we show how it is possible to derive formulas for the fair prices of many types of derivatives. Some results can actually be derived in a model-independent way, although more generally we will work within the framework of a discrete-time trading model.


  • Week 4: Topic title

    • week 4 - LECTURE

      • The term structure of interest rates.
      • Spot rates and forward rates.

       

      week 4 - TUTORIAL

       

      week 4 TASKS


  • Week 5: Topic title

    • WEEK 5 - LECTURE

      • Stochastic interest rates

       

      WEEK 5 - TUTORIAL

      WEEK 5 TASKS

      • Read Section 4 of the typed lecture notes.
      • Fill in the early-feedback questionnaire at the top of the QMPlus page (tap on the right)

    • File icon
      Coursework 3 File
      145.2 KB

      Due date: Friday 3 November


    • File icon
      Solutions for Coursework 3 File
      162.0 KB
    • Quiz icon
      Practice Quiz 2

      There are 5 questions. You may take the quiz as many times as you like. 


  • Week 6: Topic title

    • WEEK 6 - LECTURE

      • Shares, Forward and Options
      • Pricing Options: model-independent pricing principles

       

      WEEK 6 - TUTORIAL

       

      WEEK 6 TASKS

      • Take Test 1. It counts 10% of your final mark. Deadline to submit is Wednesday 1 November at 5pm.
      • Read Sections 4.3, 5.1, 5.2, and 5.3.


    • Quiz icon
      Test 1 Quiz

      This midterm test is worth 10% of your final mark for this module. The test consists of 10 questions, all weighted equally.

      The test is available from Monday 30 October  5pm to Wednesday 1 November 5pm and you must submit your answers within this time frame.


  • Week 7: Topic title

    Week 7 is Reading Week and there will be no lectures or tutorials.

  • Week 8: Topic title

  • Week 9: Topic title

    • WEEK 9 - LECTURE

      • The single period model

       

      WEEK 9 - TUTORIAL

       

      WEEK 9 TASKS

      •  Complete Coursework 4
      • Read Section 6.1 of the typed lecture notes


    • Quiz icon
      Practice Quiz 3

       There are 5 questions. You may take the quiz as many times as you like. 

  • Week 10: Topic title

  • Week 11: Topic title

    • WEEK 11 - LECTURE

      • The multi-period binomial model
      • The Black-Scholes formula 

      WEEK 11 - TUTORIAL

      WEEK 11 TASKS

      • Take Quiz 4
      • Read Chapter 7 of the typed notes
      • Complete Coursework 5

    • Quiz icon
      Practice Quiz 4

      There are 5 questions. You may take the quiz as many times as you like.

  • Syllabus

    SYLLABUS

    1. Bank accounts, money markets and fixed income
      1. Interest rates and present value analysis
      2. Arbitrage
      3. Bonds
      4. Term structure of interest rates
    2. Stochastic models for investment returns
      1. Multi-period investments with independent interest rates in each period
    3. Equity markets and their derivatives
      1. Equities (stocks and shares)
      2. Forward contracts
      3. Options (European and American)
    4. Pricing derivatives by no-arbitrage arguments
      1. Model-independent examples
      2. Pricing derivatives via the risk neutral distribution
    5. Simple option-pricing models in discrete time
      1. Single-period binomial model
      2. Replicating Portfolios
      3. Single-period general model using state price deflators
      4. Two-period binomial model
    6. The multi-period binomial model
      1. Discrete-time random processes
      2. Multi-period binomial model
    7. The Black-Scholes formula
      1. The option price as a limit of binomial models



  • Module aims and learning outcomes

    • Learning Aims and Outcomes

      ACADEMIC CONTENT

      This module covers:

      • Interest rates, rate of return and continuously varying interest rates.
      • Time value of money, present value analysis.
      • Stochastic models for investment returns.
      • Option pricing, including arbitrage.


      SKILLS TO BE LEARNED

      At the end of this module, students should be able to:

      • Describe various financial instruments.
      • Explain how probability enters modern descriptions of financial instruments.
      • Explain the time-value of money and use it to analyse simple cashflow models.
      • Explain the notion of arbitrage and apply it to determine the fair price of various financial instruments.
      • Appreciate that even the most basic of financial models requires a profound combination of techniques from various branches of mathematics.


      ATTRIBUTES

      At the end of this module, students should hopefully have developed with respect to the following attributes:

      • Acquire and apply knowledge in a rigorous way.
      • Connect information and ideas within their field of study.
      • Explain and argue clearly and concisely.
      • Apply analytical skills to investigate unfamiliar problems.
      • Acquire substantial bodies of new knowledge.



  • assessment

    This module will be assessed by

    1. Two quizzes each worth 10 marks

    2. A final exam worth 80 marks

    Both the quizzes and the final exam will be online.

  • teaching team

  • hints and tips

    Here are my tips for a successful exam.

    1) Keep up with the course. Attend all lectures. If you miss a lecture, watch it afterwards on Q-Review. Read the lecture notes.

    2) Attend all tutorials. Try the coursework questions, first yourself, and then later compare with the model solution. If you don't understand something, make yourself a note and ask the lecturer at the next available tutorial.

    3) Do the online practice quizzes. You can do these as often as you like.

    4) The online tests (counting 10% each) will be similar in style to the practice quizzes.

    5) Shortly before the final exam (counting 80%), look at a past paper as a final test for yourself, after you have finished your preparation. Don't learn past papers by heart, they were set by different lecturers. More important is that you can do questions similar to the coursework questions of the current module.


  • where to get help

    The first point of contact is your lecturer. You are very welcome to ask me questions after the lecture or during the tutorial. Or, just send me an e-mail (c.beck@qmul.ac.uk).

    I also have a learning support office hour. This is Fridays 16:00-17:00 in my office, room 121 in the Maths building. During this time, you may also contact me online, by clicking https://whereby.com/chrbeck

    There are some problem that go well beyond the scope of mathematics. Queen Mary has a dedicated council service and there you can get help and advice on all kinds of problems. Just go to https://qmul.ac.uk/welfare/     You can also call them under 020 7882 8717 (Monday-Friday 10am-4pm).


  • general course information

  • Past exam papers

    The best preparation for the exam is to regularly attend the lectures and tutorials, and to try to do the coursework questions yourself, then compare your solution with the model solution. You should also do all the practice quizzes. Then, finally, shortly before the exam takes place, you might also look at a past exam paper, although these were set by a different lecturer. Last year's exam is below.

  • Week 12: Topic title

    WEEK 12 - LECTURE

    • All lectures in week 12 will be revision lectures, summarizing the most important contents of the lecture notes, coursework questions, and practice quizzes. In the final lecture on Friday we will go through last year's exam.

    WEEK 12 - TUTORIAL

    • This very last tutorial will be more like an office hour where you can talk to me on any topic you like.

    WEEK 12 TASKS

    • Take Test 2. It counts 10% of your final mark. Deadline to submit is Wednesday 13 December at 5pm.

  • Early feedback questionnaire

  • Assessment information

    • Assessment Pattern -  There will be two tests, each counting 10%, and a final exam counting 80%.

      Format and dates for the in-term assessments - The in-term tests will be online. They will take place in week 6 and week 12. You will have a 48 hour period to do these tests. The typical time you need for each test is about 1 hour, but there will be no time limit employed, apart from the 48 hour window of availability of the tests.

      Format of final assessment - The final exam is online. It will take place on Friday 12 January 2024 at 11:00 and it will last for 3 hours. This exam will be a hybrid quiz:  The first 7 questions will be similar in style to the in-term assessments in form of a quiz, but there will be also a request to upload a hand-written solution for the final question. You have 30 additional minutes to upload the PDF file of your hand-written solution.

      Link to past papers - It is more important that you look at coursework questions and understand how to do the solutions than looking at past papers. Nevertheless, below you find a link to last year's exam paper. In the revision class given in  week 12 we will go through the solutions of that paper.

      Description of Feedback - There will also be online practice quizzes which you can take as often as you like and which do not count. These will give you immediate feedback.

       

    • File icon
      Last year's exam paper File
      102.6 KB
    • File icon
      Solutions to last year's exam paper File
      127.7 KB

  • Reading List

  • Q-Review