Our share-based payments primarily consist of stock options and restricted stock units (“RSUs”). Share-based compensation expense was as follows (in millions):

	For the Years Ended December 31,
	2020		2019		2018
Total expense, pre-tax	$	79.7	$	84.3	$	65.5
Tax benefit related to awards		16.9		21.8		14.6
Total expense, net of tax	$	62.8	$	62.5	$	50.9

We had two equity compensation plans in effect at December 31, 2020: the 2009 Stock Incentive Plan (“2009 Plan”) and the Stock Plan for Non-Employee Directors. We have reserved the maximum number of shares of common stock available for awards under the terms of each of these plans. We have registered 44.1 million shares of common stock under these plans. The 2009 Plan provides for the grant of nonqualified stock options and incentive stock options, long-term performance awards in the form of performance shares or units, restricted stock, RSUs and stock appreciation rights. The Compensation and Management Development Committee of the Board of Directors determines the grant date for annual grants under our equity compensation plans. The date for annual grants under the 2009 Plan to our executive officers is expected to occur in the first quarter of each year following the earnings announcements for the previous quarter and full year. The Stock Plan for Non-Employee Directors provides for awards of stock options, restricted stock and RSUs to non-employee directors. It has been our practice to issue shares of common stock upon exercise of stock options from previously unissued shares, except in limited circumstances where they are issued from treasury stock. The total number of awards which may be granted in a given year and/or over the life of the plan under each of our equity compensation plans is limited. At December 31, 2020, an aggregate of 6.1 million shares were available for future grants and awards under these plans.

Stock options granted to date under our plans generally vest over four years and have a maximum contractual life of 10 years. As established under our equity compensation plans, vesting may accelerate upon retirement after the first anniversary date of the award if certain criteria are met. We recognize expense related to stock options on a straight-line basis over the requisite service period, less awards expected to be forfeited using estimated forfeiture rates. Due to the accelerated retirement provisions, the requisite service period of our stock options range from one to four years. Stock options are granted with an exercise price equal to the market price of our common stock on the date of grant, except in limited circumstances where local law may dictate otherwise.

A summary of stock option activity for the year ended December 31, 2020 is as follows (options in thousands):

	Stock Options			Weighted Average Exercise Price		Weighted Average Remaining Contractual Life		Intrinsic Value (in millions)
Outstanding at January 1, 2020		7,285		$	107.53
Options granted		1,370			155.68
Options exercised		(1,028	)		100.69
Options forfeited		(175	)		135.54
Options expired		(29	)		113.53
Outstanding at December 31, 2020		7,423		$	116.67		6.3	$	282.0
Vested or expected to vest as of December 31, 2020		7,205		$	115.92		6.2	$	278.8
Exercisable at December 31, 2020		4,581		$	104.20		5.0	$	228.5

We use a Black-Scholes option-pricing model to determine the fair value of our stock options. Expected volatility was derived from a combination of historical volatility and implied volatility because the options that were actively traded around the grant date of our stock options did not have maturities of over one year. The expected term of the stock options has been derived from historical employee exercise behavior. The risk-free interest rate was determined using the implied yield currently available for zero-coupon U.S. government issues with a remaining term approximating the expected life of the options. The dividend yield was determined by using an estimated annual dividend and dividing it by the market price of our stock on the grant date.

The following table presents information regarding the weighted average fair value of stock options granted, the assumptions used to determine fair value, the intrinsic value of options exercised and the tax benefit of options exercised in the indicated year:

	For the Years Ended December 31,
	2020			2019			2018
Dividend yield		0.6	%		0.8	%		0.8	%
Volatility		22.3	%		22.1	%		22.1	%
Risk-free interest rate		1.3	%		2.4	%		2.7	%
Expected life (years)		5.0			5.5			5.2
Weighted average fair value of options granted	$	31.65		$	28.68		$	26.66
Intrinsic value of options exercised (in millions)	$	50.1		$	76.8		$	46.6
Tax benefit of options exercised (in millions)	$	9.6		$	15.8		$	6.8

As of December 31, 2020, there was $49.9 million of unrecognized share-based payment expense related to nonvested stock options granted under our plans. That expense is expected to be recognized over a weighted average period of 2.4 years.

We have awarded RSUs to certain of our employees. The terms of the awards are generally three or four years. Some of the awards have only service conditions while some have performance and market conditions in addition to service conditions. Future service conditions may be waived if an employee retires after the first anniversary date of the award, but performance and market conditions continue to apply. Accordingly, the requisite service period used for share-based payment expense on our RSUs range from one year to four years.

A summary of nonvested RSU activity for the year ended December 31, 2020 is as follows (RSUs in thousands):

				Weighted Average
				Grant Date
	RSUs			Fair Value
Outstanding at January 1, 2020		1,228		$	118.11
Granted		446			148.10
Vested		(281	)		114.35
Forfeited		(323	)		132.42
Outstanding at December 31, 2020		1,070			129.65

For the RSUs with service conditions only, the fair value of the awards was determined based upon the fair market value of our common stock on the date of grant. For the RSUs with market conditions, a Monte Carlo valuation technique was used to simulate the market conditions of the awards. The outcome of the simulation was used to determine the fair value of the awards.

We are required to estimate the number of RSUs that will vest and recognize share-based payment expense on a straight-line basis over the requisite service period. As of December 31, 2020, we estimate that approximately 646,553 outstanding RSUs will vest. If our estimate were to change in the future, the cumulative effect of the change in estimate will be recorded in that period. Based upon the number of RSUs that we expect to vest, the unrecognized share-based payment expense as of December 31, 2020 was $44.8 million and is expected to be recognized over a weighted-average period of 2.1 years. The fair value of RSUs that vested during the years ended December 31, 2020, 2019 and 2018 based upon our stock price on the date of vesting was $33.2 million, $26.3 million, and $18.7 million, respectively.