What’s in the Forecast? The Black-Scholes Formula and Forecasting Factors

If your company is in the process of assigning a formal value to equity compensation awards, it’s likely that you’re going to use the Black-Scholes-Merton model, a pricing model used to determine the fair value of stock options. The model is based on a variety of assumption calculations. Below, we’ll break down Black-Scholes assumptions piece by piece so you can gain a deeper understanding of the mathematical architecture of the pricing model.

Expected life

A lot hinges on the expected life, also known as the expected term. Expected life is the number of years after the grant date that you estimate your employee will exercise the option. Public companies that have roughly five to seven years of activity calculate this term by looking at the number of years employees have historically taken to exercise their options.

However, private companies, or newly public companies with little history, typically take their cue from SAB 107/110. Options that are considered to be “plain vanilla,” meaning they are issued in the money, exercisability is based on performing a service through the vesting date, shares are non-transferable, and terminated employees forfeit unvested shares and have a limited amount of time to exercise before cancelation. This rule sets out a simplified method for calculating expected term, which involves taking the number of years in which your awards will vest (three years, in our example) and the number of years to expiration (seven years), and averaging them (3 + 7 = 10 ÷ 2 = 5). Companies can choose another method if advised by their auditors, but the simplified method is the most common approach for private companies.

Dividend yield

Public companies arrive at this input by estimating the amount of dividends that will be paid over the expected life of the award based on historic dividend payments. Of course, because private companies that issue options don’t typically declare dividends, there’s normally no calculation at all. The dividend yield factor is simply set at zero.

Volatility

Volatility is the anticipated fluctuation of your stock price over the expected term, expressed as a percentage. In our example, calculating this with Black-Scholes volatility means determining by what percentage your stock price will go up or down over the expected five-year term. Mature public companies have relatively easy access to this input – they can use a standard volatility formula that analyzes how their exchange-traded stock prices changed over the past five years (or whatever the expected term is) to the date of the grant, and use that as an input.

Private and recently public companies, however, must once again turn to SAB 107/110, which allows them to use a public company peer group’s volatility as a proxy for their own. Typically, you’ll select between four and ten peer public companies that are similar to yours – usually selecting companies in the same or similar industry, that are a similar size, and have a similar business model or financial standing – usually using the same peer public companies that were used to prepare your company’s 409A valuation. From there, you’ll assign a weight to each company’s volatility to calculate the volatility of the closing prices for each peer company for a period equal to the expected term, take the standard deviation of these stock prices over the number of days in each trading year and average the rate (or do a more advanced weighted average) to determine volatility.

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