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Stock-Based Compensation (Tables)
 6 Months Ended
Jun. 30, 2019
Stock-Based Compensation [Abstract]  
Stock-Based Award Plan Activity A summary of the Company’s stock option (including SARs) activity for the six month period ended June 30, 2019 is presented in the following table (underlying shares in thousands).


 
Shares
    
Weighted-Average
Exercise Price
(per share)
  
Outstanding as of December 31, 2018
    
12,352
    
$
10.93
  
Granted
    
1,070
    
$
27.05
  
Exercised or settled
    
(3,890
)
  
$
8.72
  
Forfeited
    
(90
)
  
$
30.42
  
Expired
    
(9
)
  
$
32.06
  
Outstanding as of  June 30, 2019
    
9,433
    
$
13.46
  
Vested as of  June 30, 2019
    
7,266
    
$
9.61
  

Assumptions Used to Estimate Fair Value of Options Granted The following assumptions were used to estimate the fair value of options granted (excluding previously disclosed modified awards) during the six month periods ended June 30, 2019 and 2018 using the Black-Scholes option-pricing model.


 
For the Six Month
Period Ended
June 30,
2019
    
For the Six Month
Period Ended
June 30,
2018
  
Assumptions
            
Expected life of options (in years)
    
6.3
      
7.0 - 7.5
  
Risk-free interest rate
    
2.4 - 2.6
%
    
2.9 - 3.0
%
Assumed volatility
    
30.7 - 31.8
%
    
34.4 - 35.4
%
Expected dividend rate
    
0.0%
%
    
0.0%
%

Restricted Stock Unit Activity A summary of the Company’s restricted stock unit activity for the six month period ended June 30, 2019 is presented in the following table (underlying shares in thousands).


 
Shares
    
Weighted-Average
Grant-Date
Fair Value
  
Non-vested as of December 31, 2018
    
362
    
$
31.78
  
Granted
    
418
    
$
27.05
  
Vested
    
(33
)
  
$
31.97
  
Forfeited
    
(38
)
  
$
31.56
  
Non-vested as of June 30, 2019
    
709
    
$
28.97