SHARE-BASED AWARDS AND OPTIONS

The following table summarizes share-based compensation expense and the related income tax benefit recognized for our share-based awards and stock options:



	Three Months Ended				Nine Months Ended
	September 30, 2018		September 30, 2017		September 30, 2018		September 30, 2017

	(in thousands)

Share-based compensation expense	$	14,833	$	9,617	$	44,937	$	30,771
Income tax benefit	$	3,614	$	3,523	$	10,276	$	10,788

Share-Based Awards

The following table summarizes the changes in unvested restricted stock and performance awards for the nine months ended September 30, 2018:



	Shares		Weighted-Average Grant-Date Fair Value

	(in thousands)

Unvested at December 31, 2017	1,226			$78.29
Granted	600		107.16
Vested	(715	)	62.89
Forfeited	(55	)	90.40
Unvested at September 30, 2018	1,056		$104.52

The total fair value of restricted stock and performance awards vested during the nine months ended September 30, 2018 and September 30, 2017 was $45.0 million and $27.6 million, respectively.

For restricted stock and performance awards, we recognized compensation expense of $13.8 million and $8.6 million during the three months ended September 30, 2018 and September 30, 2017, respectively, and $41.1 million and $27.7 million during the nine months ended September 30, 2018 and September 30, 2017, respectively. As of September 30, 2018, there was $67.7 million of unrecognized compensation expense related to unvested restricted stock and performance awards that we expect to recognize over a weighted-average period of 2.1 years. Our restricted stock and performance award plans provide for accelerated vesting under certain conditions.

Stock Options

The following summarizes changes in stock option activity for the nine months ended September 30, 2018:



	Options		Weighted-Average Exercise Price		Weighted-Average Remaining Contractual Term	Aggregate Intrinsic Value

	(in thousands)				(years)	(in millions)

Outstanding at December 31, 2017	723			$47.79	6.4	$37.9
Granted	103		114.70
Forfeited	(9	)	81.68
Exercised	(188	)	39.40
Outstanding at September 30, 2018	629			$60.75	6.1	$41.8

Options vested and exercisable at September 30, 2018	457			$47.50	5.1	$36.5

We recognized compensation expense for stock options of $0.7 million during each of the three months ended September 30, 2018 and 2017, and $2.3 million and $2.0 million during the nine months ended September 30, 2018 and September 30, 2017, respectively. The aggregate intrinsic value of stock options exercised during the nine months ended September 30, 2018 and September 30, 2017 was $15.9 million and $9.9 million, respectively. As of September 30, 2018, we had $4.4 million of unrecognized compensation expense related to unvested stock options that we expect to recognize over a weighted-average period of 2.0 years.

The weighted-average grant-date fair value of each stock option granted during the nine months ended September 30, 2018 and September 30, 2017 was $35.09 and $23.68, respectively. Fair value was estimated on the date of grant using the Black-Scholes valuation model with the following weighted-average assumptions:



	Nine Months Ended
	September 30, 2018	September 30, 2017

Risk-free interest rate	2.60%	1.99%
Expected volatility	29%	30%
Dividend yield	0.04%	0.06%
Expected term (years)	5	5

The risk-free interest rate is based on the yield of a zero coupon U.S. Treasury security with a maturity equal to the expected life of the option from the date of the grant. Our assumption on expected volatility is based on our historical volatility. The dividend yield assumption is calculated using our average stock price over the preceding year and the annualized amount of our most current quarterly dividend per share. We based our assumptions on the expected term of the options on our analysis of the historical exercise patterns of the options and our assumption on the future exercise pattern of options.