We have a share-based compensation incentive plan that allows us to grant stock options, restricted stock, RSUs, and other awards to employees and nonemployee directors. Total shares authorized under the plan at December 31, 2023 were 4,300,000, of which 2,747,546 were available for future grants.

All share-based payments to employees, including grants of employee stock options, are recorded as compensation expense 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 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” on the consolidated statement of income, and the corresponding equity effect is included in shareholders’ equity. We account for forfeitures of share-based compensation awards as they occur. Substantially all share-based awards of stock options, restricted stock, and RSUs have graded vesting that is recognized on a straight-line basis over the vesting period.

At December 31, 2023, compensation expense not yet recognized for nonvested share-based awards was approximately $34 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 2023, 2022, and 2021, we used the Black-Scholes option pricing model to estimate the grant date value of stock options in determining compensation expense. The following schedule summarizes the weighted average value at grant date and the significant assumptions used in applying the Black-Scholes model for options granted:


	2023			2022			2021

Weighted average value for options granted	$	11.23		$	15.16		$	7.86
Weighted average assumptions used:
Expected dividend yield	3.0		%	2.3		%	2.5		%
Expected volatility	27.0		%	27.0		%	25.0		%
Risk-free interest rate	4.00		%	1.98		%	0.47		%
Expected life (in years)	4.5			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, 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
Granted	201,932	73.02
Exercised	(256,004)	36.79
Expired	(8,912)	37.58
Forfeited	(2,794)	57.75
Balance at December 31, 2022	1,262,366	50.75
Granted	291,005	52.90
Exercised	(95,207)	29.67
Expired	(27,948)	35.41
Forfeited	(9,838)	57.07
Balance at December 31, 2023	1,420,378	52.83
Outstanding stock options exercisable as of:
December 31, 2023	891,884	$	50.36
December 31, 2022	729,411	46.02
December 31, 2021	693,883	41.54

We issue new authorized common shares for the exercise of stock options. The total intrinsic value of stock options exercised was approximately $2 million in 2023, $7 million in 2022, and $16 million in 2021. Cash received from the exercise of stock options was $2 million in 2023, $8 million in 2022, and $20 million in 2021.


	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

$25.00 to $29.99	452	29.12				3.8	452	29.12

$40.00 to $44.99	73,077	44.18				0.2	73,077	44.18
$45.00 to $49.99	558,629	47.34				3.6	446,660	47.01
$50.00 to $59.99	587,155	52.78				3.8	301,194	52.67
$60.00 to $73.22	195,842	73.19				5.0	65,278	73.19


	1,420,378	52.83		1		3.7	891,884	50.36

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, 2023 and 2022 was less than $1 million and $4 million, respectively, while the aggregate intrinsic value of exercisable options was less than $1 million and $3 million at the same respective dates. For exercisable options, the weighted average remaining contractual life was 2.7 years and 2.8 years at December 31, 2023 and 2022, respectively, excluding the stock options previously noted without a fixed expiration date. At December 31, 2023, 528,192 stock options with a weighted average exercise price of $57.01, and a weighted average remaining life of 5.4 years, were expected to vest according to their respective schedules with an aggregate intrinsic value of $0.

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. Compensation expense is determined based on the number of restricted shares or RSUs granted and the market price of our common stock at the issue date. During 2023, 2022, and 2021, we granted 39,771, 16,722, and 16,938 RSUs, respectively, to nonemployee directors. The RSUs vested immediately upon grant.


	Number of shares	Weighted average fair value

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
Issued	21,038	60.21
Vested	(25,105)	42.66

Nonvested restricted shares at December 31, 2022	60,749	48.31
Issued	—	—
Vested	(24,978)	46.31

Nonvested restricted shares at December 31, 2023	35,771	49.71


	Number of restricted stock units	Weighted average fair value

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
Granted	433,674	68.07
Vested	(504,358)	47.83
Forfeited	(34,306)	56.58
Restricted stock units at December 31, 2022	1,169,093	53.62
Granted	727,019	48.85
Vested	(522,163)	48.71
Forfeited	(44,004)	56.19
Restricted stock units at December 31, 2023	1,329,945	52.88

The total value at grant date of restricted stock and RSUs vested during the year was $27 million in 2023, $25 million in 2022, and $24 million in 2021. At December 31, 2023, 35,771 shares of restricted stock and 881,923 RSUs were expected to vest according to their respective schedules with an aggregate intrinsic value of $2 million and $39 million, respectively.