OPTION PRICING THEORY

OPTION PRICING THEORY ASSIGNMENT 2003-2004

The requirements of this assignment included (a) the calculation of returns, (b) tests of the random walk hypothesis, (c) tests of serial correlation, (d) normality tests, (e) options pricing, and (f) volatilities calculation. Closing data for six UK equity stocks and the FT 100 Index provides the bases for the completion of the requirements.

Data were obtained covering the five-year inclusive period 7 December 1999 - 7 December 2004 for the equity stocks of six UK publicly traded companies included in the FT100 index, as well as the FT100 index itself. Closing index data reflecting total returns were collected on both daily and monthly bases.

Returns were calculated for each equity stock and the FT100 based on both the daily data and the monthly data. The returns were calculated as per cent gain or loss expressed as decimal fractions to the fourth decimal point. The method of calculating the returns was as follows:

Current Period Index Value - Prior Period Index Value

The results of the Step 1 calculations are summarized in Table 1 (which may be found on the following page). The data presented in the summary table are (a) mean returns (daily and monthly) and (b) standard deviations of daily returns and monthly returns. Complete sets of the calculated returns for all six equity stocks and the FT100 on both daily and monthly bases are contained

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pattern could have occurred by chance. The test includes a formula leading to the average number of runs to expect, and providing indications as to deviations from the average. This information permits quantification of the possibility that non-random patterns with some predictive are present. Randomness is rejected when the actual number of runs observed exceeds the expected number by at least two standard deviations at p<.05. The random walk hypothesis was tested in this assignment in relation to each of the six UK equity stocks (Barclays, BT Group, Dixons Group, Marks & Spencer, Tesco, and Vodafone Group) and the FT 100. The hypothesis was tested through the analysis of the daily returns and the monthly returns (discussed in the preceding section of this assignment) through application of the non-parametric runs test in the SPSS statistical application program. The results of the runs tests are summarized in Table 2 - Runs Daily Returns and Table 3 - Runs Monthly Returns (which may be found on the following page). The complete results of the runs tests performed for this assignment are contained in the attached SPSS output files (Runs Daily Returns and Runs Monthly Returns). The runs tests applied to daily returns perm

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