Share-Based Compensation

The following table presents share-based compensation expense:



	For the Three Months Ended March 31,
	2018		2019
Share-based compensation	$	10.7	$	8.8
Tax benefit	2.7		1.8

As of December 31, 2018, the Company had unrecognized share-based compensation expense of $54.1 million. As of March 31, 2019, the Company had unrecognized share-based compensation expense of $77.9 million, which will be recognized over a weighted average period of approximately two years (assuming no forfeitures).

Stock Options

The following table summarizes transactions in the Company’s stock options:



	Stock Options	Weighted Average Exercise Price		Weighted Average Remaining Contractual Life (Years)
Unexercised options outstanding - December 31, 2018	0.5	$	130.81
Options granted	0.0	110.02
Options exercised	(0.0)	107.63
Options forfeited	(0.0)	122.67
Unexercised options outstanding - March 31, 2019	0.5	130.54		3.7
Exercisable at March 31, 2019	0.4	129.01		3.4

For the three months ended March 31, 2018 and 2019, the Company granted stock options with fair values of $0.5 million in each period. Stock options generally vest over a period of three to four years and expire seven years after the grant date. All options have been granted with exercise prices equal to the closing price of the Company’s common stock on the grant date. In certain circumstances, option awards also require certain performance conditions to be satisfied in order for the options to be exercised.

The fair value of options granted was estimated using the Black-Scholes option pricing model and were $53.81 and $33.58, per option, for the three months ended March 31, 2018 and 2019, respectively. The weighted average grant date assumptions used to estimate the fair value of options granted were as follows:



	For the Three Months Ended March 31,
	2018		2019
Dividend yield	0.7	%	1.2	%
Expected volatility	24.6	%	31.9	%
Risk-free interest rate	2.6	%	2.6	%
Expected life of options (in years)	5.7		5.7
Forfeiture rate	—	%	—	%

Restricted Stock

The following table summarizes transactions in the Company’s restricted stock units:



	Restricted Stock Units		Weighted Average Grant Date Value
Unvested units - December 31, 2018	0.6		$	172.74
Units granted	0.3		110.02
Units vested	(0.2	)	169.93
Units forfeited	(0.0)		156.63
Unvested units - March 31, 2019	0.7		145.80

For the three months ended March 31, 2018 and 2019, the Company granted restricted stock unit awards with fair values of $36.7 million and $32.6 million, respectively. These awards were valued based on the closing price of the Company’s common stock on the grant date and the number of awards expected to be delivered. Awards containing vesting conditions generally require service over a period of three to four years and may also require the satisfaction of certain performance conditions. In certain cases, awards with performance conditions may use structures whereby the number of shares of the Company’s common stock that an employee ultimately receives at vesting will be equal to the base number of restricted stock units granted, multiplied by a predetermined percentage determined in accordance with the Company’s attainment of certain pre-established performance measures and could be higher or lower than the original restricted stock unit grant. During the three months ended March 31, 2019, there were no changes in the Company’s estimate of the number of shares expected to be delivered.