**Option Pricing Theory –**

#### Requirements

Choose six UK companies that have options written on them.

Stock prices can be obtained Bloomberg. Option prices can be obtained from Bloomberg.

**Step 1: **For each of your six companies download from Bloomberg 5 years of daily, weekly and monthly total returns data. The total return is just the stock price adjusted for dividends, stock splits, stock consolidations, and other capital changes.

For example, suppose stock XYZ is currently priced at 1,000 pence, and there is a dividend declared of 100 pence per share. On the ex-dividend date the share price will fall by 100 pence to 900 pence. The total returns index for the stock will adjust the price back up to 1,000 pence.

Suppose XYZ has a 10 for 1 stock split. Before the split the investor holds one share worth 1,000 pence. After the split the investor holds ten shares each worth 100 pence. The total returns index will adjust the stock price back up to 1,000 pence.

Take the end of period closing price. For example, for your weekly data take the end-of-day closing prices on a weekly basis.

**Step 2: **For each of your companies compute the daily, weekly and monthly holding period returns using 5 years of data. gives you 3 x 6 = 21 returns series altogether.

The formula is: Holding period return = (Ending price – Beginning price)/Beginning price.

**Step 3: **Test the random walk hypothesis for each series using the **runs test** on Eviews, or on any other statistical package, such as STRATA or SPSS.

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

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

**(Steps 1, 2, 3, 4 and 5 are worth 50% of the assignment grade)**

**Step 6: ****Critically discuss** the results you obtained in steps 1, 2, 3, 4 and 5.

**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.**

Option pricing theory is not free of assumptions. The option pricing methods we study in this module, the binomial tree model and the Black-Scholes formula, are only correct under the assumption that stock prices follow the random walk model.

So, Assignment 1 is all about using some real-world data to test if our basic assumptions about the random walk model are “true enough” of the real world so that we can have confidence in our option pricing techniques.

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

#### Written report

Your report should contain:

**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.

**Brief and clear**explanations of what data you used to produce your tables and how you carried out the calculations.

- 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.

**Your summary tables**

Your summary tables contain the core results you will be referring to in your critical discussion. In your report you must:

- Tell the reader exactly what the numbers in the tables stand for.

- You must tell the reader exactly what the data is used in producing your tables and where it comes from.

**There is a principle about how much detail to give. You should give enough details so that an independent researcher could download the same data, carry out the same tests, and obtain the same results.**

**Critical discussion and statistics**

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 or with your group, and then come to see Arief 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 your results by looking at them as a whole, and forming a judgement**

#### Maximum word length

2,000 words. The word limit does not include tables or references.