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Share-based Payments (Tables)
 12 Months Ended
Dec. 31, 2020
Disclosure Of Share Based Payments [Abstract]  
Schedule of Activities in RSUs, RSAs and Other Contingently Issuable Shares Outstanding and Related Information
Activity in the RSUs, RSAs, and other contingently issuable shares outstanding and related information is as follows:
RSUsRSAsOther
Number of
RSUs		Weighted
average
grant date
fair value		Number of
Awards		Weighted
average
grant date
fair value		Number of
Awards		Weighted
average
grant date
fair value
US$US$US$
Outstanding at January 1, 2018195,937 42.46 61,880 90.65 — — 
Granted14,383 168.24 — — — — 
Forfeited(15,991)34.93 — — — — 
Released(93,946)40.12 — — — — 
Outstanding at December 31, 2018100,383 63.87 61,880 90.65 — — 
Granted715,224 137.15 — — 162,320 145.21 
Forfeited(48,754)118.96 — — — — 
Released(128,503)98.52 (20,600)90.65 — — 
Outstanding at December 31, 2019638,350 134.79 41,280 90.65 162,320 145.21 
Granted1,127,149 161.50 — — 34,450 145.14 
Forfeited(91,613)143.13 — — — — 
Released(353,693)138.66 (41,280)90.65 (40,580)145.21 
Outstanding at December 31, 20201,320,193 155.98 — — 156,190 145.19 
Schedule 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, 201814,646,720 48.73 
Granted3,578,000 142.20 
Forfeited(1,220,508)62.82 
Exercised(4,736,555)40.97 
Expired(24,131)54.98 
Outstanding at December 31, 201812,243,526 77.63 
Granted4,152,565 147.11 
Forfeited(719,860)105.01 
Exercised(3,478,660)49.41 
Expired(43,799)117.79 
Outstanding at December 31, 201912,153,772 107.68 
Granted2,356,040 180.12 
Forfeited(855,051)131.30 
Exercised(4,556,908)78.87 
Expired(56,565)146.69 
Outstanding at December 31, 20209,041,288 138.60 
Exercisable at December 31, 20185,162,876 58.25 
Exercisable at December 31, 20195,553,650 84.18 
Exercisable at December 31, 20204,022,751 113.91 
Summary of Stock Options Outstanding
The stock options outstanding December 31, 2020, 2019, and 2018 are comprised of the following:
202020192018
Range of exercise prices (US$)Number of
options		Weighted
average
remaining
contractual
life (years)		Number of
options		Weighted
average
remaining
contractual
life (years)		Number of
options		Weighted
average
remaining
contractual
life (years)
1.65to45.00195,207 0.32,130,161 0.94,753,052 1.8
45.01to90.001,243,833 1.22,482,270 2.23,337,414 3.2
90.01to135.002,234,257 2.72,946,838 3.42,695,890 3.9
135.01to180.003,671,417 3.53,318,423 4.1749,360 4.3
180.01to437.631,696,574 3.61,276,080 3.7707,810 4.2
9,041,288 2.912,153,772 2.912,243,526 2.9
Summary of Black-Scholes Option-Pricing Models
The following table lists the inputs to the Black-Scholes option-pricing models used for employee share-based compensation for the years ended December 31, 2020, 2019, and 2018:
202020192018
Expected volatility (%)
30.0 – 42.8
30.1 – 35.2
32.0 – 34.7
Risk-free interest rate (%)
0.1 – 1.7
1.4 – 2.6
2.4 – 2.9
Expected life of stock options (years)
2.6 – 4.8
2.5 – 4.8
2.4 – 4.4
Weighted-average share price (US$)162.82 136.09 142.20 
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 2020:
2020
(in € millions)
Actual stock option expense30 
Stock option expense increase (decrease) under the following
   assumption changes
Volatility decreased by 10%(9)
Volatility increase by 10%9 
Expected life decrease by 1 year(6)
Expected life increase by 1 year5 
Summary of Expense Recognized in Consolidated Statement of Operations for Employee Share Based Payments
The expense recognized in the consolidated statement of operations for employee share-based compensation is as follows:
202020192018
(in € millions)
Cost of revenue8 4 3 
Research and development84 61 40 
Sales and marketing34 27 19 
General and administrative50 30 26 
176 122 88