CSCO » Topics » Lattice-Binomial Model

This excerpt taken from the CSCO 10-Q filed Nov 20, 2007.

Lattice-Binomial Model

Upon adoption of SFAS 123(R), the Company began estimating the value of employee stock options and employee stock purchase rights on the date of grant using a lattice-binomial model. Prior to the adoption of SFAS 123(R), the value of each employee stock option and employee stock purchase right was estimated on the date of grant using the Black-Scholes model.

The Company’s employee stock options have various restrictions including vesting provisions and restrictions on transfer and hedging, among others, and are often exercised prior to their contractual maturity. Lattice-binomial models are more capable of



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incorporating the features of the Company’s employee stock options than closed-form models such as the Black-Scholes model. The use of a lattice-binomial model requires extensive actual employee exercise behavior data and a number of complex assumptions including expected volatility, risk-free interest rate, expected dividends, kurtosis, and skewness. The weighted-average assumptions, using the lattice-binomial model, the weighted-average expected life and estimated value of employee stock options and employee stock purchase rights are summarized as follows:


     Three Months Ended  
     October 27,
    October 28,

Weighted-average assumptions:


Expected volatility

     30.6 %     25.9 %

Risk-free interest rate

     4.4 %     4.6 %

Expected dividend

     0.0 %     0.0 %


     4.6       4.5  


     (0.80 )     (0.80 )

Weighted-average expected life (in years)

     6.3       6.7  

Weighted-average estimated value

   $ 9.92     $ 6.88  

The determination of the fair value of share-based payment awards on the date of grant using an option-pricing model is affected by the Company’s stock price as well as assumptions regarding a number of highly complex and subjective variables. The weighted-average assumptions were determined as follows:



For employee stock options, the Company used the implied volatility for two-year traded options on the Company’s stock as the expected volatility assumption required in the lattice-binomial model, consistent with SFAS 123(R) and Staff Accounting Bulletin No. 107 (“SAB 107”). For employee stock purchase rights, the Company used the implied volatility for six-month traded options on the Company’s stock. The selection of the implied volatility approach was based upon the availability of actively traded options on the Company’s stock and the Company’s assessment that implied volatility is more representative of future stock price trends than historical volatility.



The risk-free interest rate assumption is based upon observed interest rates appropriate for the term of the Company’s employee stock options and employee stock purchase rights.



The dividend yield assumption is based on the history and expectation of dividend payouts.



The estimated kurtosis and skewness are technical measures of the distribution of stock price returns, which affect expected employee exercise behaviors that are based on the Company’s stock price return history as well as consideration of various academic analyses.

The expected life of employee stock options represents the weighted-average period the stock options are expected to remain outstanding and is a derived output of the lattice-binomial model. The expected life of employee stock options is impacted by all of the underlying assumptions and calibration of the Company’s model. The lattice-binomial model assumes that employees’ exercise behavior is a function of the option’s remaining vested life and the extent to which the option is in-the-money. The lattice-binomial model estimates the probability of exercise as a function of these two variables based on the entire history of exercises and cancellations on all past option grants made by the Company.

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