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Equity-Based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2020
Equity-Based Compensation |
Summary of RSUs | ​
​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | Weighted Average
​ | ​ | ​ | ​ | Per Share
​ |  | Units |  | Fair Value
Unvested as of January 1, 2020 |  | 348 | ​ | $ | 86.15
Granted |  | 122 | ​ | $ | 123.21
Vested |  | (125) | ​ | $ | 73.78
Forfeited |  | (14) | ​ | $ | 100.82
Unvested as of December 31, 2020 |  | 331 | ​ | $ | 103.84
Summary of PSUs | ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted Average
​ | ​ | ​ | ​ | Per Share
​ |  | Units |  | Fair Value
Unvested as of January 1, 2020 |  | 1,077 | ​ | $ | 99.66
Granted |  | 301 | ​ | $ | 153.34
Vested |  | (362) | ​ | $ | 84.54
Forfeited |  | (17) | ​ | $ | 121.81
Unvested as of December 31, 2020 |  | 999 | ​ | $ | 120.95
Summary of Stock Options | ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted Average
​ | ​ | ​ | ​ | Per Share
​ |  | Options |  | Exercise Price
Outstanding as of January 1, 2020 |  | 3,938 | ​ | $ | 69.66
Granted |  | 684 | ​ | $ | 126.01
Exercised |  | (1,039) | ​ | $ | 116.18
Forfeited or expired |  | (40) | ​ | $ | 102.11
Outstanding as of December 31, 2020 (a) |  | 3,543 | ​ | $ | 82.86
Exercisable as of December 31, 2020 (b) |  | 1,910 | ​ | $ | 62.21
(a) | Stock options outstanding as of December 31, 2020 have a weighted average remaining contractual term of 6.5 years and an aggregate intrinsic value of $130 million based on the market value of our common stock on December 31, 2020.
(b) | Stock options exercisable as of December 31, 2020 have an aggregate intrinsic value of $106 million based on the market value of our common stock on December 31, 2020.
Summary of Exercisable Stock Options | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted Average |  | ​
​ | ​ | ​ | ​ | Per Share | ​ | Weighted Average
Range of Exercise Prices |  | Options |  | Exercise Price |  | Remaining Years
$33.49-$50.00 |  | 520 | ​ | $ | 38.54 |  | 2.0
$50.01-$70.00 |  | 564 | ​ | $ | 55.53 |  | 4.7
$70.01-$100.00 |  | 825 | ​ | $ | 81.66 |  | 6.8
$100.01-$126.01 |  | 1 | ​ | $ | 126.01 |  | 9.1
$33.49-$126.01 |  | 1,910 | ​ | $ | 62.21 |  | 4.9
Weighted Average Assumptions Used to Value Employee Stock Options Granted | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | 2020 |  | 2019 |  | 2018
Expected option life |  | 4.6 | years |  | 4.2 | years |  | 4.3 | years
Expected volatility |  | 16.6 | % |  | 15.5 | % |  | 17.9 | %
Expected dividend yield |  | 1.7 | % |  | 2.1 | % |  | 2.2 | %
Risk-free interest rate |  | 1.4 | % |  | 2.5 | % |  | 2.6 | %

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