Option Pricing Models: An Overview of Lattice Models and Black-Scholes

January 21, 2019

You’ve decided it’s time go through the formal process of calculating the fair value for your equity compensation awards, and you’re trying to choose an appropriate stock option valuation model. You’re likely also discovering that keeping up to date on the latest accounting rules when it comes to calculating the fair value can be challenging. Fear not, because below, we provide a high-level overview of the two most common option pricing models: Lattice models and the Black-Scholes pricing model. After reading this blog, you should gain a better understanding of the history of each model, how each model works, and what the most commonly used model is.

Lattice models: More accurate, but more work

First, we’ll cover Lattice models. Gaining popularity in 2004, Lattice models are 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 a stock price and the probability of exercise during each interval.

A binomial lattice option pricing model takes 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, some argue that lattice models are more accurate than the Black-Scholes model detailed below. However, lattice models also take comparably more time to calculate due to the number of inputs needed. Additionally, they cost more to operate and may 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 industry standard

Black-Scholes option pricing model has been the most commonly used 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, this can also be called Black-Scholes option pricing model assumptions. It’s not possible to concretely predict the fair market value when the inputs to a lattice model are changed. Plus, a more complex model is generally only necessary when an award has a market-based performance goal, like an increase in stock price based on stock traded in the public market – which is why Black-Scholes remains a favorite of private companies.

“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 market value of equity shares. However, private companies are allowed to make a one-time accounting policy election to choose the intrinsic value method, which is extremely simple, instead of using fair value. 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 interesting, right? So why wouldn’t every single private company do that? Say a private company eventually goes public, this can 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, a company that elected the intrinsic value method will be required to change the accounting method for most compensation awards at some point. That’s why some companies argue it makes more 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. Selecting an option pricing model can be complex, but hopefully after reading this blog you have the foundational knowledge you need to move confidently through the process. In the next blog in this series, we dive into the two types of factors that go into a Black-Scholes value calculation.

If you have any questions or would like to get in touch to talk more, reach out to our team.

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