# Calculate the volatilities implied by the market prices of the options, using Derivagem.

Requirements

Choose about six UK companies that have options written on them. You will need sufficient data to be able to adequately discuss and illustrate the issues developed in the assignment, so about six should be enough. However, if you find your results are limiting your scope for discussion you may need to run the techniques for a few more companies to get additional results.

Stock prices can be obtained from Yahoo Finance UK or other free website, DataStream or Bloomberg. Option prices can be obtained from the

from Bloomberg.

Step 1: For each of your companies compute the daily, weekly and monthly returns using 5 years of data. Also compute the daily, weekly and monthly returns for the FTSE100 index. This gives you 3 x 7 = 21 returns series altogether.

Step 2: Test the random walk hypothesis for each series using the runs test on SPSS.

Step 3: Carry out a serial correlation test on the series using SPSS (or some other computer statistics package).

Step 4: Carry out a normality test on the daily, weekly and monthly returns of each company and of the index.

(Steps 1, 2, 3, and 4 are worth 25% of the assignment grade)

Step 5: Critically discuss the results you obtained in steps 1, 2, 3, and 4.

Relate the results you have obtained to the underlying assumptions made in option pricing theory, namely that stock returns follow a random walk and that stock returns are normally distributed.

Interpreting statistical results is a matter of judgement and organised commonsense. It is not a technical matter of applying another formula.

(Step 5 is worth 25% of the assignment grade)

In this part you are testing some of our basic assumptions about stock returns. You are testing whether stock returns really follow a random walk in (2) and (3), and in (4) 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.

Step 6: Compute the theoretical value of a selection of calls and puts written on your stocks using the Derivagem options pricing software. Also compute the theoretical value of one call option and one put option using the Black-Scholes formula.

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 6 is worth 25% of the assignment grade)

Step 7: Calculate the volatilities implied by the market prices of the options, using Derivagem. By calculating implied volatilities on selected options, do you find evidence of mispricing in the options market? If so, explain at least two strategies for exploiting this apparent mispricing. Critically discuss.

(Step 7 is worth 25% of the assignment grade)

Written report

Write a report. Your report should contain:

(1) A clear summary of your results.

(2) A brief and clear explanation of how you carried out the calculations.

(3) A critical discussion of your results and conclusions.

The requirements (1), (2) and (3) are very important. Make sure you try to achieve these in your written report.

For example, using clearly presented tables to summarise your results in (1) is good. Spending pages and pages describing in detail what the reader can clearly see from the tables is bad.

If you write a poorly structured report with a bunch of spreadsheets/printouts attached at the end, it is very difficult for the examiner to know what your results are, whether you have carried out the calculations correctly, what your conclusions are, and in general, whether or not you understand what you are doing.

Your aim in writing your report must be to convince the reader that you have complete confidence in applying these techniques, that you understand the ideas behind these applications, and that you can critically discuss the results and form reasonable conclusions.

Hints and mistakes to avoid

In general, we will give help and feedback in showing how to use the techniques, but the discussion, explanation and interpretation required in the report is mostly up to you. If you add up the marks you will see that around 50% of the assignment grade is for explanation, discussion and interpretation. This should be reflected in your report.

Try to do the statistical tests first yourself, and then come to see us if you get stuck.

When discussing the results from the statistical tests and from the option pricing calculations, it is important that your report does not simply describe the results you get. Simply listing the results is something that is best done by putting them in a table.

When interpreting the results of statistical tests, you need to consider what the results say overall. This is an art, not a science. Some people think that interpreting statistical results means applying another formula. It isn’t. It is a matter of judgement, on which experts themselves often disagree. So, don’t be concerned that you do not know enough statistics to interpret the results. A lot of it is just looking at the results as a whole and using common sense.

You must interpret the results of this assignment by looking at them as a whole, and forming a judgement

Maximum word length

Your report must be between 1,500 and 2,500 words in length

As a general rule, shorter is usually better. In this kind of material it is possible to say all the important things concisely, briefly, simply and clearly.