how to calculate volatility for Black Scholes?

Yes, most of us will use the Black Scholes model to value our stock option grants (or the equity portion of a convertible note). The other inputs are fairly straight forward but most often than not I am asked how to calculate (or find!) volatility? Well, it all depends on if you are public or private.

Public

Because you are traded on an open market volatility can be calculated quite easily. Historical volatility is used as a proxy for the expected volatility. Black Scholes assumes that financial asset prices are random variables that are lognormally distributed. Therefore, returns to financial assets, i.e. the relative price changes, are usually measured by the difference in log prices, which will be normally distributed (e.g. a bell curve). This is the Log Relative price. Stock prices are usually observed at fixed intervals of time (e.g. daily, weekly or monthly) and we then have a time series of data (e.g. on September 4 the stock closed at $0.11 and a week later on September 10 the stock closed at $0.12). Therefore, to get the Log Relative price you would use the following formula in excel:

=LN(September 4th price/September 10th price) or =LN(0.11/0.12)

The historical volatility is the volatility of a series of stock prices where we look back over the historical price path of the particular stock. To enable us to compare volatilities for different interval lengths we usually express volatility in annual terms. So, if daily data is used the interval is one trading day or 252 intervals, a week is 52 intervals and monthly is 12 intervals. Volatility is simply the standard deviation of the sampled series (over how many intervals) and can be expressed as follows for weekly in excel:

=STDEV(Log Relative series as calculated above)*SQRT(52)

Business Ready guides their clients to use a weekly data series, for a one year period, as pulled from Yahoo Finance and exported to excel for the above analysis.

Private

Per CICA 3870, paragraph 35, and FAS 123(R), section 3.2, non-public entities can elect to not estimate volatility (e.g. value of 0) because it is not practicable due to insufficient information available. That was easy!

I hope this helps. If you need to see an example, download the Business Ready Stock Option Calculator and look at the volatility example.