# Option Pricing Models: Which One Is Right for You?

January 21, 2019

So, you’ve decided it’s time go through the formal process of calculating fair value for your equity compensation awards, and you’re trying to choose an appropriate pricing model. Around about now, you’re likely discovering that you haven’t exactly kept up on the latest accounting rules on stock option valuation. Fear not! Keep reading for a high-level overview of the two most common option pricing models – lattice models (which come in two flavors) and Black-Scholes – so you can determine which one is best for your company.

## Lattice models: More accurate, but more work

Lattice models became the talk of the town around 2004. They’re defined by their inclusion of a greater number of data inputs than more traditional valuation models. In essence, they break down the life of each grant into small intervals and determine the option value depending on the potential movement of your stock price and the probability of exercise during each interval.

A binomial lattice model takes – you guessed it –  two possibilities into account: whether the stock price goes up or down. A trinomial lattice model assumes your stock price will either go up, down, or remain flat during each interval. At each interval, the model looks at the potential movement of your stock price to determine when your employees will most likely exercise their options. At each interval, both (or all three) possible outcomes are calculated – resulting in hundreds or thousands of possibilities.

Because they analyze numerous data sets, lattice models have been touted as more accurate than the Black-Scholes model detailed below. However, lattice models also take more time to calculate due to the number of inputs and, correspondingly, they cost more to operate and take more time to justify to your auditors. Plus, most private companies don’t have the necessary stock price and exercise history required to make valid complex calculations. For these reasons, Black-Scholes is an industry standard for both private and public companies and it looks to remain so.

## Black-Scholes: The tried and true

The go-to option pricing model since roughly 1994, Black-Scholes (sometimes called the Black-Scholes-Merton model) assumes that your employees will exercise all their options on a single day at the end of the expected life of the award. Notably, with Black-Scholes, your company defines that “expected life” period – usually looking at historic transactions to estimate the amount of time between the grant date and the date the employee exercises the option. This differs from lattice models, where the estimated “expected life” is one of the model outputs.

As an algebraic formula, Black-Scholes gives stakeholders greater comfort by making outputs predictable. In contrast, it’s not possible to concretely predict the final value when the inputs to a lattice model are changed. And, finally, the only time more complex model is required is when an award has a market-based performance goal, like an increase in stock price based on stock traded in the public market.

## “Intrinsic” value: When does it come into play?

At the end of the day, both the lattice and Black-Scholes models will get you to fair value. However, private companies are allowed to make a one-time accounting policy election to choose the intrinsic value method, which is extremely simple. Intrinsic value is calculated by taking the company’s stock price on the measurement date (usually the grant date) and subtracting the amount the employee has to pay for the award, if any.

Pretty slick, right? So why wouldn’t every single private company do that? Assuming a private company eventually goes public, this will be a troublesome election. Public companies must use a fair value measurement for stock options, SSARs and the majority of their equity compensation awards. So if an IPO is in the cards, that means a company that elected the intrinsic value method will be required to change the accounting method for most compensation awards at some point – which is why it makes better sense to use a fair value calculation from the start. Yes, we did say most compensation awards. Full value awards, such as restricted stock awards and restricted stock units, can only be accounted for using intrinsic value.

### Still unclear?

Selecting an option pricing model can be complex but here’s an easy test:

• Do you have 7 years or less of option exercise history?
• Are vested options usually held instead of exercised?
• Do you have 5 years or less of at least quarterly stock valuations?
• Do you have lots of money to spend on running your chosen award valuation method?

If you answer yes to the first three questions and no to the fourth, your auditor will likely recommend the Black-Scholes option pricing model. And since most other companies use that model, you’ll be in good company. Next in this series we’ll decipher the two types of factors that go into a Black-Scholes value calculation.

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