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Stock Compensation (Tables)

12 Months Ended

Dec. 31, 2019

Stock Compensation

Schedule of valuation assumptions used for valuation of fair value of stock compensation granted

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​	​	​	​	​	​	​	​	​	​	​	​	​	​
​	​	Employee Stock Options					​	Employee Stock Purchase Plan					​
​	​	For the year ended December 31,					​	For the year ended December 31,					​
​		2019		2018		2017		2019		2018		2017	​
Average risk-free interest rates	​	2.27	%	2.61	%	1.80	%	1.82	%	2.62	%	1.53	%
Average expected life (in years)	​	5.27	​	5.26	​	5.25	​	0.50	​	0.50	​	0.50	​
Volatility	​	45	%	45	%	49	%	31	%	46	%	38	%
Weighted-average fair value (in dollars)	​	32.38	​	34.20	​	53.41	​	14.04	​	15.80	​	19.42	​

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- Definition

Tabular disclosure of the significant assumptions used during the year to estimate the fair value of employee stock options plan and employee stock purchase plans, including, but not limited to: (a) expected term, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions.

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