v3.25.0.1
Share-based compensation (Tables)
 12 Months Ended
Dec. 31, 2024
Disclosure Of Share Based Payments [Abstract]  
Summary of Activities in RSUs and Other Contingently Issuable Shares Outstanding and Related Information
Activity in the Group’s RSUs and other contingently issuable shares outstanding and related information is as follows:
RSUsOther
Number of
RSUs		Weighted
average
grant date
fair value		Number of
Awards		Weighted
average
grant date
fair value
US$US$
Outstanding at January 1, 20221,425,196 211.25 108,720 145.19 
Granted2,914,248 121.42 30,824 162.21 
Forfeited(359,238)173.04 (20,357)145.21 
Released(844,799)173.76 (47,470)145.20 
Outstanding at December 31, 20223,135,407 142.23 71,717 152.50 
Granted1,379,324 121.77 — — 
Forfeited(657,607)134.72 — — 
Released(1,302,199)143.68 (34,819)148.96 
Outstanding at December 31, 20232,554,925 132.39 36,898 155.83 
Granted732,639 273.40 — — 
Forfeited(135,153)153.67 — — 
Released(1,132,039)156.28 (14,596)154.15 
Outstanding at December 31, 20242,020,372 168.81 22,302 156.93 
Summary of Activity in Stock Options Outstanding and Related Information
Activity in the stock options outstanding and related information is as follows:
Options
Number of
options		Weighted
average
exercise price
US$
Outstanding at January 1, 20228,695,348 190.19 
Granted9,640,611 141.55 
Forfeited(1,332,946)215.07 
Exercised(620,143)78.33 
Expired(377,980)130.86 
Outstanding at December 31, 202216,004,890 164.56 
Granted2,140,650 129.05 
Forfeited(1,647,782)158.21 
Exercised(3,057,801)128.91 
Expired(1,010,712)190.86 
Outstanding at December 31, 202312,429,245 165.93 
Granted663,407 284.32 
Forfeited(264,246)155.41 
Exercised(5,933,613)169.47 
Expired(204,366)310.28 
Outstanding at December 31, 20246,690,427 170.49 
Exercisable at December 31, 20226,402,109 172.69 
Exercisable at December 31, 20235,793,791 184.98 
Exercisable at December 31, 20242,520,115 189.66 
Summary of Stock Options Outstanding
The stock options outstanding at December 31, 2024, 2023, and 2022 are comprised of the following:
202420232022
Range of exercise prices (US$)Number of
options		Weighted
average
remaining
contractual
life (years)		Number of
options		Weighted
average
remaining
contractual
life (years)		Number of
options		Weighted
average
remaining
contractual
life (years)
25.01to45.00— 0752 0.12,289 1.1
45.01to90.00723,791 2.81,101,330 3.71,147,396 4.8
90.01to135.001,997,219 2.83,362,206 3.34,036,371 3.3
135.01to180.002,100,527 2.44,639,068 2.76,741,590 3.1
180.01to498.981,856,703 2.53,325,889 2.14,077,244 3.0
498.99to715.4412,187 4.8— 0— 0
6,690,427 2.612,429,245 2.816,004,890 3.3
Summary of Black-Scholes Option-Pricing Models
The following table lists the inputs to the Black-Scholes option-pricing models used for stock options for the years ended December 31, 2024, 2023, and 2022:
202420232022
Expected volatility (%)
49.9 – 57.6
51.5 – 61.2
35.9 – 60.0
Risk-free interest rate (%)
3.5 – 4.9
3.5 – 4.9
0.9 – 4.5
Expected life of stock options (years)
2.6 – 4.8
2.6 – 4.8
2.6 – 4.8
Weighted-average share price (US$)275.89 128.33 124.47 
Summary of Impact of Changes on Stock Options Expense for Options Granted The following table shows the impact of these changes on stock option expense for the options granted in 2024:
2024
(in € millions)
Actual stock option expense30 
Stock option expense increase/(decrease) under the following
   assumption changes
Volatility decreased by 10%(4)
Volatility increase by 10%4 
Expected life decrease by 1 year(5)
Expected life increase by 1 year4 
Summary of Expense Recognized in Consolidated Statement of Operations for Employee Share Based Payments
The expense recognized in the consolidated statement of operations for share-based compensation is as follows:
202420232022
(in € millions)
Cost of revenue5 5 8 
Research and development152 194 218 
Sales and marketing61 66 73 
General and administrative49 56 82 
Total267 321 381