Volatility

Volatility is the measure of the amount by which a variable fluctuates or is expected to fluctuate in a given period of time. Since an option grant is a right to buy the common stock at a future date for a set price, option pricing models require an assumption that predicts how the underlying common stock will fluctuate during this future time period. This is commonly referred to as an estimate of the expected volatility.


Expected volatility should be based on historical volatility, but should be adjusted if the historical data is not indicative of future expectations, such as is the case with private entities. Due to the nature of a private entity, often times there is insufficient data on historical stock prices, making it difficult to determine a reasonable historical volatility. For this reason, companies may consider using an industry sector or public peer company data when estimating the expected volatility.


For all privately held entities and some public entities with limited historical trading data, Carta requires clients to list their public peers prior to generating their ASC718 report, ASC 718 requires the entity to identify the specific companies used as the peers. Public entities with sufficient trading data will be prompted to use their own trading data to estimate historical volatility. 


Carta uses the peer company approach by taking the average volatility of at least four peer companies. An example of the function used is displayed below:

In essence, this function is mimicking the historical volatility approach for the entity’s peer companies and averaging it amongst all peers used. In order to generate sufficient historical data, the function extracts the daily closing price from the measurement date and backtracks by the expected term. The closing prices are adjusted for events such as dividends, stock splits, etc. As an example, if a grant’s measurement date started on January 1, 2014 and has a remaining life of five years, we would extract up to five years of historical data from January 1, 2009 to January 1, 2014. We then determine the change in the closing price for each day and the standard deviation from the mean. We then will have 5 year worth of data compiling the standard deviation. The last step is then to annualize this number so that it reflects 1 year. This is exemplified by multiplying the standard deviation by the square root of 252 days.  We repeat this process for the rest of the peer companies and average the data to arrive at an applicable volatility for your company. In cases where some of the public peer companies used do not have enough relevant data, that specific company may or may not be excluded from our calculations.

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