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Equity-Based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2019
Equity-Based Compensation |
Summary of RSUs | Restricted Stock Units — A summary of our RSUs is presented in the table below (units in thousands):
​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | Weighted Average
​ | ​ | ​ | ​ | Per Share
​ |  | Units |  | Fair Value
Unvested as of January 1, 2019 |  | 392 | ​ | $ | 70.52
Granted |  | 121 | ​ | $ | 99.91
Vested |  | (151) | ​ | $ | 56.74
Forfeited |  | (14) | ​ | $ | 86.11
Unvested as of December 31, 2019 |  | 348 | ​ | $ | 86.15
Summary of PSUs | ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted Average
​ | ​ | ​ | ​ | Per Share
​ |  | Units |  | Fair Value
Unvested as of January 1, 2019 |  | 1,164 | ​ | $ | 90.17
Granted |  | 364 | ​ | $ | 116.26
Vested |  | (427) | ​ | $ | 93.03
Forfeited |  | (24) | ​ | $ | 98.33
Unvested as of December 31, 2019 |  | 1,077 | ​ | $ | 99.66
Summary of Stock Options | ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted Average
​ | ​ | ​ | ​ | Per Share
​ |  | Options |  | Exercise Price
Outstanding as of January 1, 2019 |  | 4,441 | ​ | $ | 59.46
Granted |  | 839 | ​ | $ | 98.90
Exercised |  | (1,278) | ​ | $ | 107.96
Forfeited or expired |  | (64) | ​ | $ | 83.20
Outstanding as of December 31, 2019 (a) |  | 3,938 | ​ | $ | 69.66
Exercisable as of December 31, 2019 (b) |  | 2,063 | ​ | $ | 52.90
(a) | Stock options outstanding as of December 31, 2019 have a weighted average remaining contractual term of 6.5 years and an aggregate intrinsic value of $174 million based on the market value of our common stock on December 31, 2019.
(b) | Stock options exercisable as of December 31, 2019 have an aggregate intrinsic value of $126 million based on the market value of our common stock on December 31, 2019.
Summary of Exercisable Stock Options | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted Average |  | ​
​ | ​ | ​ | ​ | Per Share | ​ | Weighted Average
Range of Exercise Prices |  | Options |  | Exercise Price |  | Remaining Years
$33.49-$50.00 |  | 829 | ​ | $ | 37.94 |  | 2.6
$50.01-$70.00 |  | 809 | ​ | $ | 55.58 |  | 5.7
$70.01-$98.90 |  | 425 | ​ | $ | 76.98 |  | 7.5
$33.49-$98.90 |  | 2,063 | ​ | $ | 52.90 |  | 4.8
Weighted Average Assumptions Used to Value Employee Stock Options Granted | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | 2019 |  | 2018 |  | 2017
Expected option life |  | 4.2 | years |  | 4.3 | years |  | 3.5 | years
Expected volatility |  | 15.5 | % |  | 17.9 | % |  | 15.3 | %
Expected dividend yield |  | 2.1 | % |  | 2.2 | % |  | 2.3 | %
Risk-free interest rate |  | 2.5 | % |  | 2.6 | % |  | 1.7 | %

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