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# Derivatives: Option Pricing Theory – Assignment 2

#### Hand-in date for the assignment

The hand-in date for the Option Pricing Theory assignment is on or before 23.55 Friday 29 January 2021.

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Introduction

Assignment 2 follows on directly from the work you have done in Assignment 1. In Assignment 1 you tested whether the random walk and normality assumptions hold for the four stocks with options written on them.

In Assignment 2 you are applying the Black-Scholes formula and the binomial tree technique to these same securities. You are testing how well option pricing theory work when applied to some real world data.

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.

As with Assignment 1, the lectures and seminar classes will be covering topics directly related to the Assignment 2 requirements. In these classes we will be discussing the assignment in detail, and again, it is recommended that you carry out those steps in the assignment at the same time we are covering that topic in the classes.

You will be applying the binomial tree method using the Derivagem Excel software. We will be explaining and discussing how to use this software in the seminar classes.

In Assignment 2 you will be using data from Data File 2, which contains bid and ask quotes on options written on the stocks.

Step 7:

• For each of your four companies, choose 6 calls and 6 puts with the same maturity across a range strike prices.

Compute the theoretical value these of calls and puts using the binomial tree method using Derivagem.

In Step 7 (A) you should estimate the stock volatility to input into Derivagem using the data in Data File 1. Follow the technique used in John Hull – Fundamentals of Futures and Options Markets, 8th edition, Chapter 13, Section 13.4 – Estimating Volatility from Historical Data (This is the edition available online on Moodle. Other editions contain the same worked example in the Black-Scholes chapter).

• Compare the theoretical values and current market prices of the options. On the basis of this (limited) piece of empirical research, do market prices appear to be consistent with theory? Critically discuss.

(Step 7 is worth 40% of the assignment grade)

Step 8: Choose any one of your four companies. For this company choose one call and one put with the same maturity and the same strike price.

Using the same stock volatility estimate used in Step 7, calculate the theoretically correct price of the options using the Black-Scholes formula. You can do the calculations on the spreadsheet to be submitted with your report, but you should give a summary of the results in your report.

(Step 8 is worth 20% of the assignment grade)

Step 9: Using Derivagem, calculate the volatilities implied by the market prices of the calls and puts you used in Step 6. Graph each of the 8 volatility smiles.

Do these results provide evidence of mispricing in the options market? Explain your answer. Then go on to explain at least two strategies for exploiting this apparent mispricing.

(Step 9 is worth 40% of the assignment grade)

#### 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 29 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