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Option Model Assumptions

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Option Model Assumptions

The screenshot in Figure 2 below illustrates the assumptions input on the 'Option Assumptions' sheet.

Figure 2. The inputs into the Binomial Model. The input assumptions define the model computation behavior and valuation. The output values are shown for in the yellow fields: the key outputs are the Per Option Valuation and the Imputed Life.

The Binomial Lattice model requires a set of inputs to produce the output data points:

  • Total Options Granted: the total number of options in the grant.
  • Stock price at Grant Date: the actual market price when the option grant becomes effective
  • Exercise (strike) price:closing stock price on the date that the grant becomes effective.
  • Risk-Free Interest Rate: the theoretical interest rate a 'risk-free' debt instrument would earn. This is used to compute the Net Present Value of a future option exercise.
  • Suboptimal Exercise Factor: a factor multiplied by the strike price to find the prevailing stock price a option holder could be expected to exercise their option (provides a floor stock price that a stock option could be exercised during the contractual life).
  • Contractual Term (Years): The number of years the option contract is in effect (usually 10 years but some option contracts may be different. The maximum supported value is 10 years).
  • Termination Rate: The annual percentage of options assumed forfeited due to employee termination.
  • Lattice Model: The specific volatility computation method that produces the potential up and down stock values generated at each node. The values include the 'Cox, Ross & Rubenstein' or CRR and the 'Equal Probabilities' or EP models. The CRR model uses an exponent that emphasizes upward stock prices but smooths downward movement. The EP model creates equal pricing movement for both up and down movements. The CRR model is the default as it is more widely accepted because it produces slightly more conservative valuations than the EP model.
  • Volatility Table: the list of expected Volatility that is used in the Lattice model to compute upward and downward stock price movements. May be altered each year of the contractual term to better reflect anticipated trends. Please see our Volatility Tool. This powerful tool can compute the volatility number using historical stock data.
  • Dividend Yield Table: the annualized dividend yield paid on the stock at the end of each annual period.
  • Annual Vesting Table: the percentage of the option grant that vests each year.
  • Blackout Checkbox: if checked, no options granted may be exercised in each year regardless of stock price.
  • Mid-Year Exercise on Sub-Optimal Price: if checked, the grantee is assumed to exercise all vested options at the sub-optimal price when the stock reaches or exceeds that price at year-end. This option enables the model to simulate mid-year exercise following the sub-optimal exercise assumption. If not checked, grantees are assumed to exercise at the year-end stock price if that price is greater than the sub-optimal price.

The Binomial Lattice model creates a wide array of potential outcomes for stock prices and option exercise behavior using these input assumptions. The Sub-Optimal Exercise factor assumption informs the model when an option grantee can be expected to exercise their available shares and when the computed stock price exceeds this value (Sub-Optimal Exercise factor x Option Strike price).

The Volatility input for each year informs the model on how much the stock price will increase or decrease in each year throughout the term. The selected Lattice model defines how the entered volatility data is used to create up/down stock price values throughout the contractual term (see the Volatility Tool for more information).

The Dividend Yield is deducted against the stock price at the end of the annual term to adjust for dividends received by stockholders, but not by option holders. Finally, the Vesting Schedule and blackout inputs control the number of options available for exercise in each year.

The result of all of this processing is a tree structure illustrated in Figure 1. Each potential outcome that creates an exercise will produce (and value) the number of vested options at the prevailing stock price less the strike price. If the stock never reaches the Sub-Optimal price but is higher than strike price at the end of the contractual term, the option will then be assumed to have exercised at that final value. Options that are "not in the money" at the end of the contractual term are valued at 0.

Each exercise on a given outcome branch will have a year and value that produces an NPV based on the input assumption Risk-Free rate to create a present-value of the potential future exercise. Each such outcome is then averaged along with outcomes that never exercise due to below strike price outcomes.

This sheet also includes record keeping entries to organize and manage multiple grants and other features to prevent accidental changes. The following information is tracked for each grant:

  • Grant Name: a short descriptive name for the grant.
  • Grant Creation Date: the effective date of the grant.
  • Grant Status: a list of possible states for the grant (Active, Cancelled, etc.)
  • Activate Grant checkbox: check this box to indicate that the grant is active an no changes should be allowed (the 'Lock Assumption' button provides a similar function but does not prevent the model from being re-calculated).

To help make using the model as straightforward as possible, help text is available for the inputs with the buttons marked with . The volatility help window is shown in the Figure 3 screenshot below.

Figure 3. The Volatility inputs into the Binomial Model and a Help screen for Volatility. Multiple values are entered for the Volatility for each year to allow the user to define stock behavior over the contractual life.

When you are ready to create a valuation, use the 'Update Model' button to take the assumptions and create the Binomial Lattice model valuation. The model creates a detailed and data-intensive set of stock pricing and option exercise scenarios to produce this valuation.

The first step in the calculation is to test the inputs for invalid data. If any inputs are out of range, an error message indicates what input is incorrect and the accepted range for that assumption. If all of the inputs are within the correct range, the model is computed and the data entered into the data output fields.

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