Suppose a data point was left out because its was an outlier, then that would be a standard practice. Some times people leave out recession periods or war periods of data in their timeseries. So, one option is just to leave it out. Another option is to use an average or interpolated value for the missing period.
You should be mindful that your choice does not interfere with the randomness of your data. For instance, look at the serial correlation (Durbin-Watson) test results for different choices you have made.
@Lall B. Ramrattan in the case of small illiquid stock markets in Africa I think it could be as a result of lack of trading activity on certain days. This also creates outliers. If there were no trades on a certain day then I suppose one could take the previous days close? I also like you suggestion to interpolate or use an average. I was worried that doing that would affect the randomness of the data....
You seem to be on the right train of thought on the issue. Keep in mind that you should document what you do. What you do will also depends on the kind of statistical results you get.
To deal with missing data depends on how many missing data you have. In case you have few it is much better to skip it, in contrary you will calculate the average price between the previous price and the next one.
I actually discovered that stock markets like Eqypt, Tunisia and Qatar don't trade on Friday's, as a result they appear to have missing values for Friday when compared to markets like SA, Nigeria and Botswana. I was surprised to find that the Morrocan market does trade on Friday though.