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SHARE-BASED AWARDS AND STOCK OPTIONS
 9 Months Ended
Sep. 30, 2023
Share-Based Payment Arrangement [Abstract]  
SHARE-BASED AWARDS AND STOCK OPTIONS SHARE-BASED AWARDS AND STOCK OPTIONS
The following table summarizes share-based compensation expense and the related income tax benefit recognized for our share-based awards and stock options:
Three Months EndedNine Months Ended
September 30, 2023September 30, 2022September 30, 2023September 30, 2022
(in thousands)
Share-based compensation expense$36,624 $37,052 $173,325 $122,465 
Income tax benefit$7,488 $10,318 $39,378 $26,816 
 
Share-Based Awards

The following table summarizes the changes in unvested restricted stock and performance awards for the nine months ended September 30, 2023:
SharesWeighted-Average
Grant-Date
Fair Value
(in thousands)
Unvested at December 31, 20222,145 $159.04 
Replacement awards202 98.44 
Granted1,311 112.83 
Vested(1,006)158.95 
Forfeited(119)130.88 
Unvested at September 30, 20232,533 $131.27 

The total fair value of restricted stock and performance awards vested during the nine months ended September 30, 2023 and September 30, 2022 was $159.9 million and $128.8 million, respectively.

For restricted stock and performance awards, we recognized compensation expense of $33.7 million and $34.5 million during the three months ended September 30, 2023 and 2022, respectively, and $153.6 million and $113.2 million during the nine months ended September 30, 2023 and 2022, respectively. As of September 30, 2023, there was $190.6 million of unrecognized compensation expense related to unvested restricted stock and performance awards that we expect to recognize over a weighted-average period of 1.9 years.
Stock Options

The following table summarizes stock option activity for the nine months ended September 30, 2023: 
OptionsWeighted-Average Exercise PriceWeighted-Average Remaining Contractual TermAggregate Intrinsic Value
(in thousands)(years)(in millions)
Outstanding at December 31, 20221,139 $111.75 5.4$17.3
Replacement awards142 98.44 
Granted233 110.83 
Forfeited(297)155.49 
Exercised(280)89.98 
Outstanding at September 30, 2023937 $99.09 5.2$24.3
Options vested and exercisable at September 30, 2023654 $96.03 3.8$19.7

We recognized compensation expense for stock options of $1.7 million and $1.2 million during the three months ended September 30, 2023 and 2022, respectively, and $15.5 million and $4.8 million during the nine months ended September 30, 2023 and 2022, respectively. The aggregate intrinsic value of stock options exercised during the nine months ended September 30, 2023 and 2022 was $8.7 million and $4.2 million, respectively. As of September 30, 2023, we had $7.1 million of unrecognized compensation expense related to unvested stock options that we expect to recognize over a weighted-average period of 1.9 years.

The weighted-average grant-date fair value of stock options granted, including replacement awards granted in connection with the EVO acquisition, during the nine months ended September 30, 2023 and 2022 was $46.17 and $48.88, respectively. Fair value was estimated on the date of grant using the Black-Scholes valuation model with the following weighted-average assumptions:
Nine Months Ended
September 30, 2023September 30, 2022
Risk-free interest rate3.84%1.87%
Expected volatility45%40%
Dividend yield0.81%0.56%
Expected term (years)55

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 was 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.