We have a share-based compensation incentive plan which allows us to grant stock options, restricted stock, RSUs, and other awards to employees and nonemployee directors. Total shares authorized under the plan were 9,000,000 at December 31, 2021, of which 1,889,694 were available for future grants.

All share-based payments to employees, including grants of employee stock options, are recognized in the income statement based on their grant date values with consideration of service and performance vesting requirements. The value of an equity award is estimated on the grant date using a fair value-based model without regard to service or performance vesting conditions, but does consider post-vesting restrictions.

We classify all share-based awards as equity instruments. Compensation expense is included in salaries and employee benefits in the statement of income, with the corresponding increase included in additional paid-in capital. We account for forfeitures of share-based compensation awards as they occur. Substantially all awards of stock options, restricted stock, and RSUs have graded vesting that is recognized on a straight-line basis over the vesting period.

Compensation expense and the related tax benefit for all share-based awards were as follows:


(In millions)	2021		2020		2019

Compensation expense	$	28	$	26	$	27
Reduction of income tax expense	11		8		11

We reduced share-based compensation expense by $2 million during 2021, and by $1 million during both 2020 and 2019, as a result of using a valuation model to estimate a liquidity discount on RSUs with post-vesting restrictions.

As of December 31, 2021, compensation expense not yet recognized for nonvested share-based awards was approximately $28 million, which is expected to be recognized over a weighted average period of 2.4 years.

Stock options granted to employees generally vest at the rate of one third each year and expire seven years after the date of grant. For all stock options granted in 2021, 2020, and 2019, we used the Black-Scholes option pricing model to estimate the grant date value of stock options in determining compensation expense. The following summarizes the weighted average value at grant date and the significant assumptions used in applying the Black-Scholes model for options granted:


	2021			2020			2019

Weighted average value for options granted	$	7.86		$	8.18		$	10.30
Weighted average assumptions used:
Expected dividend yield	2.5		%	3.0		%	2.5		%
Expected volatility	25.0		%	27.0		%	26.0		%
Risk-free interest rate	0.47		%	1.38		%	2.52		%
Expected life (in years)	5.0			5.0			5.0

The assumptions for expected dividend yield, expected volatility, and expected life reflect management’s judgment and include consideration of historical experience. Expected volatility is based in part on historical volatility. The risk-free interest rate is based on the U.S. Treasury yield curve in effect at the time of grant for periods corresponding with the expected life of the option.


	Number of shares	Weighted average exercise price

Balance at December 31, 2018	2,004,598	$	29.85
Granted	256,818	50.80
Exercised	(569,808)	24.61
Expired	(4,330)	22.37
Forfeited	(10,500)	43.13
Balance at December 31, 2019	1,676,778	34.77
Granted	320,913	45.61
Exercised	(285,954)	26.48
Expired	(22,685)	30.17
Forfeited	(5,395)	51.34
Balance at December 31, 2020	1,683,657	38.26
Granted	345,636	48.65
Exercised	(686,894)	31.08
Expired	(7,910)	42.16
Forfeited	(6,345)	48.04
Balance at December 31, 2021	1,328,144	44.60
Outstanding stock options exercisable as of:
December 31, 2021	693,883	$	41.54
December 31, 2020	1,137,596	33.42
December 31, 2019	1,239,821	28.95

We issue new authorized common shares for the exercise of stock options. The total intrinsic value of stock options exercised was approximately $16 million in 2021, $3 million in 2020, and $13 million in 2019. Cash received from the exercise of stock options was $20 million in 2021, $7 million in 2020, and $13 million in 2019.

Additional selected information on stock options at December 31, 2021 follows:


	Outstanding stock options						Exercisable stock options
Exercise price range	Number of shares	Weighted average exercise price			Weighted average remaining contractual life (years)		Number of shares	Weighted average exercise price

$4.15 to $19.99	5,223	$	6.41	1		0	5,223	$	6.41
$20.00 to $24.99	124,427	20.99				1.1	124,427	20.99
$25.00 to $29.99	89,283	29.02				0.4	88,831	29.02

$40.00 to $44.99	117,972	43.92				2.1	116,817	43.93
$45.00 to $49.99	633,124	47.27				5.6	80,518	45.66
$50.00 to $55.68	358,115	52.75				3.5	278,067	53.20



	1,328,144	44.60		1		3.9	693,883	41.54

1 The weighted average remaining contractual life excludes 5,223 stock options without a fixed expiration date that were assumed with the Amegy acquisition. They expire between the date of termination and one year from the date of termination, depending upon certain circumstances.

The aggregate intrinsic value of outstanding stock options at December 31, 2021 and 2020 was $25 million and $14 million, respectively, while the aggregate intrinsic value of exercisable options was $15 million and $14 million at the same respective dates. For exercisable options, the weighted average remaining contractual life was 2.6 years and 2.2 years at December 31, 2021 and 2020, respectively, excluding the stock options previously noted without a fixed expiration date. At December 31, 2021, 632,759 stock options with a weighted average exercise price of $47.95, a weighted average remaining life of 5.4 years, and an aggregate intrinsic value of $10 million, were expected to vest.

Restricted stock is common stock with certain restrictions that relate to trading and the possibility of forfeiture. Generally, restricted stock vests over four years. Holders of restricted stock have full voting rights and receive dividend equivalents during the vesting period. In addition, holders of restricted stock can make an election to be subject to income tax on the grant date rather than the vesting date.

RSUs represent rights to one share of common stock for each unit and generally vest over four years. Holders of RSUs receive dividend equivalents during the vesting period, but do not have voting rights.

During 2021, 2020, and 2019, we granted 16,938, 28,992, and 19,116 RSUs, respectively, to nonemployee directors. The RSUs vested immediately upon grant.

The following summarizes our restricted stock activity for the three years ended December 31, 2021:


	Number of shares	Weighted average fair value

Nonvested restricted shares at December 31, 2018	45,686	$	33.78
Issued	24,994	42.83
Vested	(20,223)	30.69

Nonvested restricted shares at December 31, 2019	50,457	39.50
Issued	27,798	45.65
Vested	(20,859)	34.77

Nonvested restricted shares at December 31, 2020	57,396	44.20
Issued	26,083	39.16
Vested	(18,663)	43.89

Nonvested restricted shares at December 31, 2021	64,816	42.26

The following summarizes our RSU activity for the three years ended December 31, 2021:


	Number of restricted stock units	Weighted average fair value

Restricted stock units at December 31, 2018	1,400,699	$	37.65
Granted	536,489	47.85
Vested	(614,968)	33.74
Forfeited	(28,150)	44.69
Restricted stock units at December 31, 2019	1,294,070	43.59
Granted	586,302	42.75
Vested	(593,375)	37.56
Forfeited	(44,676)	47.78
Restricted stock units at December 31, 2020	1,242,321	46.31
Granted	578,056	47.02
Vested	(505,690)	46.51
Forfeited	(40,604)	47.97
Restricted stock units at December 31, 2021	1,274,083	46.49

The total value at grant date of restricted stock and RSUs vested during the year was $24 million in 2021, $23 million in 2020, and $21 million in 2019. At December 31, 2021, 64,816 shares of restricted stock and 847,876 RSUs were expected to vest with an aggregate intrinsic value of $4 million and $54 million, respectively.