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,
	2020		2019		2018

	(in thousands)

Share-based compensation expense	$	148,792	$	89,634	$	57,826
Income tax benefit	$	33,530	$	20,519	$	13,038

Restricted stock awards vest in equal annual installments over a three-year period or 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-based restricted stock units that, after a performance period, may convert into common shares ("performance units"). The number of common shares is dependent upon the level of achievement of certain performance measures during the performance period. The Compensation Committee of our board of directors ("Compensation Committee") establishes performance measures and may set a range of possible performance-based outcomes for performance units. Performance units are converted only after the Compensation Committee certifies performance based on pre-established measures.

For these awards, we recognize compensation expense on a straight-line basis over the applicable performance or service period using the grant date fair value of the award and the number of shares expected to be earned according to the level of achievement of performance measures. When the estimated number of common shares expected to be earned is changed during the performance period, we make a cumulative adjustment to share-based compensation expense based on the revised estimate. The performance periods for awards granted generally range from one to three years.

The following table summarizes the changes in unvested restricted stock awards and performance units for the years ended December 31, 2020, 2019 and 2018:


	Shares	Weighted-Average Grant-Date Fair Value

	(in thousands)

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
Granted	607	191.20
Vested	(835)	128.91
Forfeited	(70)	168.40
Unvested at December 31, 2020	1,546	$176.71

The total fair value of restricted stock and performance awards vested was $107.7 million, $82.1 million and $43.4 million for the years ended December 31, 2020, 2019 and 2018, respectively.

For restricted stock awards and performance units, we recognized compensation expense of $135.4 million, $74.3 million and $53.2 million for the years ended December 31, 2020, 2019 and 2018, respectively. As of December 31, 2020, there was $179.5 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 2.0 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, 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
Granted	124	200.42
Forfeited	(3)	112.85
Exercised	(623)	59.78		85.8
Outstanding at December 31, 2020	1,253	$93.66	6.3	$152.6

Options vested and exercisable at December 31, 2020	859	$71.15	5.4	$123.9

We recognized compensation expense for stock options of $8.4 million, $12.5 million and $2.7 million during the years ended December 31, 2020, 2019 and 2018, respectively. The aggregate intrinsic value of stock options exercised during the years ended December 31, 2020, 2019 and 2018 was $85.8 million, $28.8 million and $16.5 million. As of December 31, 2020, we had $8.4 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 during the years ended December 31, 2020, 2019 and 2018, including the Replacement Awards granted during the year ended December 31, 2019, was $54.85, $99.56, and $35.09, 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,
	2020		2019		2018

Risk-free interest rate	1.24	%	1.72	%	2.60	%
Expected volatility	30	%	31	%	29	%
Dividend yield	0.39	%	0.04	%	0.04	%
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 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 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.