The Binomial Lattice model produces three key outputs (see Figure 4):

• Per Option Grant Valuation: the actual stock price on the effective date for the option grant (shown with 6 digits precision to use in follow-on calculations).
• Total Grant Valuation: the contractual strike price for the options in the grant.
• Imputed Life: the average life of the grant taking into consideration that some options will exercise early (because they reached the sub optimal stock price) and yet others will be outstanding for the entire contractual term.

The model also computes statistics based on the stock behavior for each year in the contractual term. These statistics are used to compare volatility and other input assumptions based on the resulting stock prices..

Figure 4. The output and statistics produced by the Binomial Lattice model for the inputs in the previous screen shots.

The most important difference between the Black-Scholes and Binomial Lattice models is that Black-Scholes relies upon a single outcome using an assumed imputed life and only upward stock movements based on volatility. The screenshot shown in Figure 5 demonstrates a summarized example set of stock price and exercise outcomes based on the inputs created in the previous screenshots.

Figure 5. The stock price and exercise outcomes produced by the Binomial Lattice model for the inputs in the previous screen shots. For brevity, only the first few rows for outcomes in years 8 through 10 and the resulting calculations are shown. For a 10 year contractual term, the model may produce over 1,000 outcomes (depending on inputs and predicted stock behavior).

While the output may appear daunting, the most important information is the Per Option Valuation and the imputed life as shown in Figures 2 and 4. You will use these data points (along with a computed forfeiture rate) to record each grant.