We have granted nonqualified stock options and restricted stock awards to key employees, officers and directors under a long-term incentive plan, which permits grants of equity to employees, officers, directors and consultants. A total of 14.0 million shares of our common stock has been reserved and made available for issuance pursuant to awards granted under the plan. The awards are held in escrow and released upon the grantee's satisfaction of conditions of the award certificate.

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



	Years Ended December 31,
	2019		2018		2017

	(in thousands)

Share-based compensation expense	$	89,634	$	57,826	$	39,095
Income tax benefit	$	20,519	$	13,038	$	13,849

Restricted stock awards vest in equal annual installments over a three-year period and in some cases vest at the end of a three-year service period. Restricted shares cannot be sold or transferred until they have vested. The grant date fair value of restricted stock awards, which is based on the quoted market value of our common stock on the grant date, is recognized as share-based compensation expense on a straight-line basis over the vesting period.

Certain of our executives have been granted performance units under our long-term incentive plan. Performance units are performance-based restricted stock units that, after a performance period, may convert into common shares, which may be restricted. The number of shares is dependent upon the achievement of certain performance measures during the performance period. The target number of performance units and any market-based performance measures are set by the compensation committee of our board of directors ("Compensation Committee"). Performance units are converted only after the compensation committee certifies performance based on pre-established goals.

The Compensation Committee may set a range of possible performance-based outcomes for performance units. For awards with only performance conditions, we recognize compensation expense on a straight-line basis over the performance period using the grant date fair value of the award, which is based on the number of shares expected to be earned according to the level of achievement of performance goals. If the number of shares expected to be earned were to change at any time during the performance period, we would make a cumulative adjustment to share-based compensation expense based on the revised number of shares expected to be earned. The performance periods for awards granted generally range from one to three years.

To the extent earned, these performance units convert into unrestricted shares after performance results are certified by the Compensation Committee. We recognize share-based compensation expense based on the grant-date fair value of the performance-based restricted stock units, as determined by use of a Monte Carlo model, on a straight-line basis over the performance period.

The following table summarizes the changes in unvested restricted stock awards and performance units for the years ended December 31, 2019, 2018 and 2017:



	Shares		Weighted-Average Grant-Date Fair Value

	(in thousands)

Unvested at December 31, 2016	1,263		$49.55
Granted	899		79.79
Vested	(858	)	39.26
Forfeited	(78	)	59.56
Unvested at December 31, 2017	1,226		78.29
Granted	650		109.85
Vested	(722	)	60.08
Forfeited	(70	)	91.47
Unvested at December 31, 2018	1,084		108.51
Replacement Awards	894		163.74
Granted	784		142.26
Vested	(781	)	105.04
Forfeited	(137	)	124.30
Unvested at December 31, 2019	1,844		$149.96

The total fair value of restricted stock and performance awards vested was $82.1 million, $43.4 million and $33.7 million for the years ended December 31, 2019, 2018 and 2017, respectively.

For restricted stock awards and performance units, we recognized compensation expense of $74.3 million, $53.2 million and $35.2 million for the years ended December 31, 2019, 2018 and 2017, respectively. As of December 31, 2019, there was $142.9 million of unrecognized compensation expense related to unvested restricted stock awards and performance units that we expect to recognize over a weighted-average period of 2.1 years. Our restricted stock and performance unit plans provide for accelerated vesting under certain conditions.

Stock options are granted with an exercise price equal to 100% of fair market value of our common stock on the date of grant and have a term of ten years. Stock options vest in equal installments on each of the first three anniversaries of the grant date. Our stock option plans provide for accelerated vesting under certain conditions.



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

	(in thousands)			(years)	(in millions)

Outstanding at December 31, 2016	759		$37.51	6.0	$24.5
Granted	124		79.45
Exercised	(160	)	23.50		10.1
Outstanding at December 31, 2017	723		47.79	6.4	37.9
Granted	103		114.70
Forfeited	(22	)	100.38
Exercised	(206	)	42.65		16.5
Outstanding at December 31, 2018	598		59.16	6.2	27.3
Replacement Awards	1,336		68.96
Granted	109		128.22
Forfeited	(23	)	110.13
Exercised	(265	)	33.99		28.8
Outstanding at December 31, 2019	1,755		$74.06	6.5	$190.3

Options vested and exercisable at December 31, 2019	1,167		$58.03	5.6	$145.3

We recognized compensation expense for stock options of $12.5 million, $2.7 million and $2.6 million during the years ended December 31, 2019, 2018 and 2017, respectively. The aggregate intrinsic value of stock options exercised during the years ended December 31, 2019, 2018 and 2017 was $28.8 million, $16.5 million and $10.1 million. As of December 31, 2019, we had $10.3 million of unrecognized compensation expense related to unvested stock options that we expect to recognize over a weighted-average period of 1.7 years.

The weighted-average grant-date fair value of stock options granted, including Replacement Awards, during the years ended December 31, 2019, 2018 and 2017 was $99.56, $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:



	Years Ended December 31,
	2019		2018		2017

Risk-free interest rate	1.72	%	2.60	%	1.99	%
Expected volatility	31	%	29	%	30	%
Dividend yield	0.04	%	0.04	%	0.06	%
Expected term (years)	5		5		5

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