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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
STOCK-BASED COMPENSATION

Stock-based compensation granted includes stock options, performance stock awards, restricted stock awards and deferred directors’ compensation. Stock-based compensation expense was as follows:
 
Three Months Ended September 30,
 
Nine Months Ended September 30,
 
2018
 
2017
 
2018
 
2017
 
($ in millions)
Stock-based compensation
$
4.1

 
$
3.0

 
$
15.0

 
$
14.5

Mark-to-market adjustments
(1.4
)
 
2.6

 
(5.7
)
 
3.9

Total expense
$
2.7

 
$
5.6

 
$
9.3

 
$
18.4



The fair value of each stock option granted, which typically vests ratably over three years, but not less than one year, was estimated on the date of grant, using the Black-Scholes option-pricing model with the following weighted-average assumptions:
Grant date
2018
 
2017
Dividend yield
2.43
%
 
2.69
%
Risk-free interest rate
2.72
%
 
2.06
%
Expected volatility
32
%
 
34
%
Expected life (years)
6.0

 
6.0

Weighted-average grant fair value (per option)
$
8.89

 
$
7.78

Weighted-average exercise price
$
32.94

 
$
29.82

Shares granted
927,000

 
1,621,000



Dividend yield was based on our current dividend yield as of the option grant date. Risk-free interest rate was based on zero coupon U.S. Treasury securities rates for the expected life of the options. Expected volatility was based on our historical stock price movements, as we believe that historical experience is the best available indicator of the expected volatility. Expected life of the option grant was based on historical exercise and cancellation patterns, as we believe that historical experience is the best estimate of future exercise patterns.