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# Derivatives: Option Pricing Theory – Assignment 1

#### Hand-in date for the assignment

The hand-in date for the Option Pricing Theory assignment is on or before 23.55 Friday 15 January 2021.

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Introduction

The purpose of this assignment is to extend your understanding of option pricing theory by applying the theory of option pricing to some real world data.

Because of COVID, this year your Bloomberg training will be delivered in Teaching Block 2. Because of this the data required for the assignment are given to you in two Excel files, Data File 1 and Data File 2. The Data Files are in the Assignment section on the Moodle site for Option Pricing Theory. For Assignment 1 you will use only the data in Data File 1.

Both assignments require going through a series of steps. Each step requires some calculations to be carried out, as well as some critical discussion of the results obtained.

From Teaching Week 6 onwards the lectures and seminar classes will be covering topics directly related to the assignment requirements. In these classes we will be discussing the assignment detail, and it is recommended that you carry out those steps in the assignment at the same time we are covering that topic in the classes.

Fundamental assumptions of the binomial tree method and the Black-Scholes formula are that stock prices follow a Brownian motion process, i.e. a random walk with an upward drift.

In Assignment 1 you are testing these basic assumptions about stock returns. You are testing whether stock returns really follow a random walk in Steps 2, 3, 4 and 5, and in Step 6 you are testing whether stock returns really are normally distributed. In other words, you are testing whether Brownian motion is a good model for stock returns.

The statistical tests you will be using will be explained and discussed in the lecture videos and seminar classes.

#### Requirements

Data File 1 contains 5 years of daily, weekly, and monthly prices for eight UK companies that have options written on their shares. You will be carrying out the computations for four companies.

Step 1: Choose any four companies. DO NOT CHOOSE THE PRACTICE EXAMPLE, EXAMPLE PLC. Copy the data for those companies into your own spreadsheet.

Step 2:

• For each of your four companies compute the average daily, weekly and monthly returns using the 5 years of data.

• For each of your companies compute the daily, weekly and monthly variances.

• Convert the daily, weekly, and monthly returns from Parts (A) and (B) to an annual basis. Convert the daily, weekly, and monthly variances to an annual basis.

• Using a variance ratio analysis, are the results you have obtained in Part (C) consistent with the random walk hypothesis? Discuss.

Step 3: Test the random walk hypothesis for each series using the runs test on Eviews or other statistical package.

Are the results you have obtained consistent with the random walk hypothesis? Discuss.

Step 4: Test the random walk hypothesis by carrying out a serial correlation test on the series.

Are the results you have obtained consistent with the random walk hypothesis? Discuss.

Step 5: Carry out a normality test on the daily, weekly and monthly returns of each company and of the index.

Are the results you have obtained consistent with the assumption that securities returns follow a normal distribution. Discuss.

Note that we will be discussing the logic behind these statistical tests in the lectures and seminars.

Step 6: Looking at the results you have obtained as whole from Steps 2 to 5, are these consistent with underlying assumptions made in option pricing theory, namely that stock returns follow a random walk and that stock returns are normally distributed. Discuss.

#### Written report

• Clear summary tables of your key results. These should be given in the body of your report, not in an appendix. The key results are those you will be referring to in your critical discussion.

You must make it clear to the reader exactly what the numbers in the tables stand for.

• A critical discussion of your results and conclusions, as asked for in the assignment, based on the results you report in your summary tables of results.

#### Word limit

1,500 words

Group work

This is an individual assignment. However, you can work with a friend or with a group of friends when working on the computations and the interpretation of results. If you work with a friend you can use the FTSE 100 results as an independent check on your calculations.

However, you must also have at least 2 different stocks from any other member of your group.

#### Hand-in date for the assignment

The hand-in date for the Option Pricing Theory assignment is on or before 23.55 Friday 15 January 2021.

Submission

You should submit your written report and an Excel spreadsheet of you calculations on Turnitin.

Table: University of Portsmouth General Grading Criteria for Level 7 & 8

 Level 7 & 8 80+ As below plus: §  Excellent work – able to express an original reasoned argument in a lucid manner by reviewing and critiquing a wide range of material. Original, critical thinking based on outstanding insight, knowledge and understanding of material. Material contributes to current understanding and is of potentially publishable quality in terms of presentation and content. §  Wide reaching research showing breadth and depth of sources. 70-79 60-69 As below plus: §  Clear, balanced coherent critical and rigorous analysis of the subject matter. Detailed understanding of knowledge and theory expressed with clarity. §  Extensive use of relevant and current literature to view topic in perspective, analyse context and develop new explanations and theories. 50-59 As below plus: §  Detailed review and grasp of pertinent issues and a critical contextual overview of the literature. Thorough knowledge of theory and methods and uses this to underpin arguments and conclusions. §  Confidence in understanding and using literature. 40-49 §  Demonstrates grasp of key concepts and an ability to develop and support an argument in a predominately descriptive way with valid conclusions drawn from the research. §  Familiarity with key literature which is cited and presented according to convention. §  Logical and clear structure, well organised with good use of language and supporting material 30-39 FAIL – Some knowledge of relevant concepts and literature but significant gaps in understanding and / or knowledge. Little attempt at evaluation, conclusions vague, ambiguous and not based on researched material. Limited or inappropriate research. Deficits in length, structure, presentation and / or prose. 0-29