The Company’s stock-based awards that result in compensation expense consist of stock options and restricted stock units (RSUs). As of December 31, 2019, the Company had 17,300,802 shares available for grant. Stock options are granted with an exercise price equal to the market value of the Company’s common stock at the grant date and generally vest over four or five years based upon continuous employment and expire ten years from the grant date. RSUs generally vest upon three years of continuous employment or incrementally over such three-year period. Participants are not entitled to dividends on RSUs.



	Shares (in thousands)		Weighted- Average Exercise Price		Weighted- Average Remaining Contractual Term (in years)	Aggregate Intrinsic Value (in thousands)
Outstanding as of December 31, 2018	13,789		$	31.73
Granted	2,990		51.25
Exercised	(3,018	)	21.40
Forfeited or expired	(862	)	42.53
Outstanding as of December 31, 2019	12,899		$	37.95	7.14	$	236,318
Exercisable as of December 31, 2019	4,775		$	26.67	5.61	$	141,277
Options vested or expected to vest as of December 31, 2019 (1)	11,724		$	36.84	7.00	$	227,779

(1) In addition to the vested options, the Company expects a portion of the unvested options to vest at some point in the future. Options expected to vest are calculated by applying an estimated forfeiture rate to the unvested options.

The fair values of stock options granted in each period presented were estimated using the following weighted-average assumptions:



	Year Ended December 31,
	2019		2018		2017
Risk-free rate	2.7	%	2.9	%	2.4	%
Expected dividend yield	0.39	%	0.35	%	0.40	%
Expected volatility	37	%	39	%	41	%
Expected term (in years)	5.3		5.4		5.4

The risk-free rate was based upon a treasury instrument whose term was consistent with the contractual term of the option.

Generally, the current dividend yield is calculated by annualizing the cash dividend declared by the Company’s Board of Directors and dividing that result by the closing stock price on the grant date.

The expected volatility was based upon a combination of historical volatility of the Company’s common stock over the contractual term of the option and implied volatility for traded options of the Company’s stock.

The weighted-average grant-date fair value of stock options granted was $18.62 in 2019, $20.84 in 2018, and $15.59 in 2017.

The total intrinsic value of stock options exercised was $90,762,000 in 2019, $52,629,000 in 2018, and $136,672,000 in 2017. The total fair value of stock options vested was $38,974,000 in 2019, $31,106,000 in 2018, and $21,519,000 in 2017.



	Shares (in thousands)		Weighted- Average Grant Date Fair Value
Nonvested as of December 31, 2018	—		$	—
Granted	151		48.61
Vested	—		—
Forfeited or expired	(1	)	45.20
Nonvested as of December 31, 2019	150		$	48.63

The Company stratifies its employee population into two groups: one consisting of senior management and another consisting of all other employees. The Company currently applies an estimated forfeiture rate of 9% to all unvested options for senior management and a rate of 12% for all other employees. Each year during the first quarter, the Company revises its forfeiture rate. This resulted in a decrease to compensation expense of $499,000 in 2019, an increase to compensation expense of $1,283,000 in 2018, and a decrease to compensation expense of $673,000 in 2017.

As of December 31, 2019, total unrecognized compensation expense related to non-vested stock-based awards, including stock options and RSUs, was $53,491,000, which is expected to be recognized over a weighted-average period of 1.66 years.

The total stock-based compensation expense and the related income tax benefit recognized was $45,589,000 and $7,756,000, respectively, in 2019, $41,090,000 and $7,317,000, respectively, in 2018, and $31,942,000 and $10,473,000, respectively, in 2017. No compensation expense was capitalized in 2019, 2018, or 2017.

The following table presents the stock-based compensation expense by caption for each period presented on the Consolidated Statements of Operations (in thousands):



	Year Ended December 31,
	2019		2018		2017
Cost of revenue	$	1,504	$	2,447	$	1,881
Research, development, and engineering	15,748		14,578		11,022
Selling, general, and administrative	28,337		24,065		19,039
	$	45,589	$	41,090	$	31,942