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Stock-Based Compensation
9 Months Ended
Sep. 30, 2018
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Stock-Based Compensation
14.
Stock–Based Compensation
The fair value of restricted stock units (“RSUs”), deferred stock units (“DSUs”), performance-based restricted stock units (“PBRSUs”), service-based stock options and market performance-based stock options awarded during the three and nine months ended September 30, 2018 totaled $4.7 million and $34.8 million, respectively, as compared to $0.4 million and $45.7 million, respectively, for the three and nine months ended September 30, 2017. Grant activity during the nine months ended September 30, 2017 includes certain market performance-based stock options awarded to members of senior management.
The fair value of RSUs, DSUs and PBRSUs is based on the closing market price of the Company’s stock on the grant date as reported by the NYSE. The fair value of each service-based stock option award is estimated on the grant date using a Black-Scholes-Merton option-pricing model. During the first half of 2017, we granted market performance-based stock options for which we estimated the grant date fair value using a Monte-Carlo simulation model that simulated a distribution of future stock price paths based on historical volatility levels.
The table below summarizes the assumptions used to calculate the fair value of service-based stock options by year of grant:
 
 
2018
 
2017
Weighted average expected life (in years)
 
6.0

 
6.0

Weighted average exercise price
 
$
158.23

 
$
104.95

Expected stock price volatility
 
27.35
%
 
30.67
%
Risk-free interest rate
 
2.69
%
 
2.13
%
Weighted average fair value
 
$
51.27

 
$
35.58