The Six Inputs of an Option Pricing Model

Before we begin, it’s important that we discuss what exactly is fair value. In the context of stock options, fair value, not to be confused with fair market value, is essentially the estimated worth of the option. This estimation takes into account multiple factors such as fair market value, expected volatility, and other pertinent factors that we will be elaborating on later in this article.  
 
The overarching aim of fair value is to provide the company with a best-educated guess of what an option will eventually cost them for accounting purposes, and there are two primary components that constitute fair value: 

Intrinsic Value: This is the immediate value of the option if exercised at any given moment. It's the difference between the current stock price and the option's exercise price. 

Time Value: This reflects the potential of the stock to gain value over time. An option's worth can increase simply because there's more time left for the stock to appreciate before the option expires. 

In essence, the fair value is the amount an investor would be willing to pay in order to acquire the award and an option pricing model is pivotal in determining what that exactly is.  

Valuation Inputs in Option Pricing Models 

While the Black-Scholes model is the most commonly used, there are multiple different types of option-pricing models available and while ASC 718 does not specify a preference, it does require that any option-pricing model incorporate the following six factors.  

Exercise Price 

As its core, the exercise price or “strike” price of an option is the pre-agreed price at which an option holder can purchase the underlying shares associated with their award.  

Consider this example: A company grants an employee stock option with an exercise price of $25 when the fair market value at the time is also $25. Initially, the option does not have any intrinsic value as the award has yet to appreciate above the exercise price, but as market conditions evolve and company share price begins to vary, the difference between the market price and the exercise price will determine the potential profitability of the award and hence its intrinsic value.   

Under ASC 718, expense for equity awards is based on the fair value of the award at grant. Thus, even though, in my example, the intrinsic value of the option will grow as the company’s stock price increases, this doesn’t affect the expense recognized for the option (unless the company modifies the terms of the option in a way that triggers a revaluation for accounting purposes). 

Expected Life

This option-pricing model input represents a period of time in which the options granted are expected to remain outstanding before they are exercised or expire unexercised. This projection captures the behavioral tendencies of option holders and bridges the gap between grant date and the anticipated exercise or forfeiture date. 

Consider this example: An employee has been granted a stock option with an exercise price of $25 and the FMV at the time of grant is also $25. Now, based on historical data, company policy, and other relevant factors, it has been determined that the average time employees tend to hold onto their options before exercise or expiration, is six years, this estimate then becomes the expected life or term of the option.   

Private companies, newly public companies, and others that do not have sufficient data to determine the expected life of their granted stock options can determine their expected life by averaging the sum of the vesting period and the contractual life of the option. For example, if an option has a vesting period of four years and a total contractual term of 10 years, the expected term under the simplified method would be calculated as (4+10)/2 = 7 years. 

Please be aware though that this method can only be used for “plain-vanilla” stock options, which are generally awards that are subject only to service-based based vesting conditions and are exercisable for only a short time after termination of employment. There is not an exact duration for how long a company may rely on this approach, but it is expected that companies will transition to historical analysis once they have enough historical data to work off of. 

The longer the expected life of an award, the more value it will have, as the longer the expected life of an option, the more exposure the underlying stock will have to market volatility (and the more opportunity for the option holder to realize a gain on the option). This leads me into our next input. 

Expected Volatility 

At its core, volatility measures the degree to which the price of an underlying stock is expected to fluctuate within the expected life of an option. It captures the stock's price variability and provides insights into the potential price movement the stock might experience, either upwards or downwards. In option pricing, the higher the volatility, the greater the chance that the option will end up in-the-money (where exercising the option is profitable). 

Consider this example: An employee is granted a stock option with an exercise price of $25. If the underlying stock has high volatility, there's a chance the stock price might surge to $50, $75, or even higher. Conversely, it might also plummet to $10, $5, or even lower. This wide range of potential outcomes means there's a substantial possibility of the option being deeply in-the-money at some point, making it more valuable. 

However, there is some nuance to understand here, as while increased volatility does expose the option to just as much downside as it does upside, it disproportionately increases the value of the option. This is because an option provides the right, but not the obligation, to buy the underlying shares. If the stock's price dives, the option holder can simply choose not to exercise the option. In essence, the value of an option can never go below zero. So, while the downside is capped, the potential upside, thanks to high volatility, is not and this asymmetry in the payoff structure means that options inherently become more valuable as volatility increases. 

Risk-Free Interest Rate 

The risk-free interest rate quantifies the return one could expect from a completely risk-free investment over the expected life of the option. This rate signifies the value of the opportunity the option holder has to invest their capital elsewhere during the expected life option while still realizing the same appreciation in the underlying stock that they would have if they purchased the stock on the option grant date. 
 
An increase in the risk-free interest rate typically coincides with an increase to the fair value of an option while a decrease in the risk-free interest rate typically decreases it. 

Consider this example: A company grants an employee a stock option with an expected life of five years. To accurately estimate the option's value, the risk-free rate used would align with a similar term. Typically, this rate would be derived from U.S. Treasury securities because of their 'risk-free' nature. If a five-year U.S. Treasury bond offers a 2% return, then 2% becomes the input for the option pricing model. 

Expected Dividend Yield 

Within option pricing models, the expected dividend yield is the forecasted dividend payout on the underlying stock over the option's expected life. The expected dividend yield is usually found by comparing the latest dividend to the current stock price or by averaging several past dividends and comparing that to the stock prices when those dividends were announced. The important thing to note is that a higher dividend yield will tend to decrease an option's fair value, while a lower one will increase it.  

Essentially, as the expected dividend yield grows, the option's fair value drops since dividends limit the stock's potential appreciation, impacting potential upside of an option. 
 
Consider the following examples: Company XYZ has a stock price of $100 and a recent dividend of $2 per share, resulting in a 2% expected dividend yield and an employee receives a stock option priced at $100. 

In Scenario A: With a consistent $2 dividend, the option's value is calculated with a 2% yield, slightly reducing its worth due to the capped stock upside. 

In Scenario B: If Company X's dividends are rising and expected to increase to 2.5%, the option's potential value further decreases. 

More Information

As evidenced by this article, the inputs involved in option-pricing models are rather robust and the information provided is meant to provide a high-level overview. We encourage all readers to leverage the plethora of resources we have on the NASPP website and would recommend beginning with our guide to the accounting treatment of stock-based compensation linked below. 
 
NASPP | Accounting for Equity Compensation in the United States