The 2013 Equity Plan authorizes the issuance of various types of share-based awards to the Company’s employees, officers, directors, and other eligible participants. As of December 31, 2020, a total of 2,300,000 shares of the Company’s class A common stock were authorized for issuance under the 2013 Equity Plan. As of December 31, 2020, there were 415,238 shares of class A common stock reserved and available for future issuance under the 2013 Equity Plan.

Under the 2013 Equity Plan, the Company has issued stock option awards, restricted stock units, and other stock-based awards. Regardless of the type of award issued, any shares issued under the 2013 Equity Plan may consist in whole or in part of authorized but unissued shares or treasury shares. No awards may be issued more than 10 years after the 2013 Equity Plan’s effective date. In determining related share-based compensation expense for any award under the 2013 Equity Plan, the Company has made an accounting policy election to account for forfeitures of awards as they occur and therefore share-based compensation expense presented below has not been adjusted for any estimated forfeitures.

Stock options that are granted under the 2013 Equity Plan must have an exercise price equal to at least the fair market value of the Company’s class A common stock on the date of grant, become exercisable as established by the Board of Directors or the Compensation Committee, and expire no later than 10 years following the date of grant. The Company recognizes share-based compensation expense associated with such stock option awards on a straight-line basis over the award’s requisite service period (generally, the vesting period). The stock option awards granted to date vest in equal annual installments over an approximately four-year vesting period (unless accelerated in connection with a change in control event under specified conditions as set forth in the applicable option agreement or otherwise in accordance with provisions of the 2013 Equity Plan or applicable option agreement).

Share-based compensation expense related to stock option awards is based on the fair value of the stock option awards on the date of grant, as estimated using the Black-Scholes option pricing model. The Black-Scholes option pricing model requires the input of certain management assumptions, including the expected term, expected stock price volatility, risk-free interest rate, and expected dividend yield. The Company estimates the term over which option holders are expected to hold their stock options by using the simplified method for “plain-vanilla” stock option awards because the Company’s stock option exercise history does not provide a reasonable basis to compute the expected term for stock options granted under the 2013 Equity Plan. The Company has relied exclusively on its historical stock price volatility to estimate the expected stock price volatility over the expected term because the Company believed at the date of grant that future volatility was unlikely to differ from the past. In estimating the expected stock price volatility, the Company uses a simple average calculation method. The risk-free interest rate is based on U.S. Treasury securities with terms that approximate the expected term of the stock options. The expected dividend yield is based on the Company’s past cash dividend history and anticipated future cash dividend payments. The expected dividend yield is zero, as the Company has not previously declared cash dividends and does not currently intend to declare cash dividends in the foreseeable future. These assumptions are based on management’s best judgment, and changes to these assumptions could materially affect the fair value estimates and amount of share-based compensation expense recognized.

As of December 31, 2020, there were options to purchase 1,157,375 shares of class A common stock outstanding under the 2013 Equity Plan. The following table summarizes the Company’s stock option activity (in thousands, except per share data and years) for the periods indicated:

	Stock Options Outstanding
				Weighted Average		Aggregate		Weighted Average
				Exercise Price		Intrinsic		Remaining Contractual
	Shares			Per Share		Value		Term (Years)
Balance as of January 1, 2018		992		$	145.28
Granted		710			130.27
Exercised		(21	)		121.13	$	196
Forfeited/Expired		(201	)		154.49
Balance as of December 31, 2018		1,480			137.16
Granted		470			150.88
Exercised		(51	)		128.17	$	799
Forfeited/Expired		(265	)		135.88
Balance as of December 31, 2019		1,634			141.60
Granted		118			146.76
Exercised		(348	)		146.80	$	29,994
Forfeited/Expired		(247	)		146.63
Balance as of December 31, 2020		1,157		$	139.48
Exercisable as of December 31, 2020		644		$	135.05	$	163,318	4.1
Expected to vest as of December 31, 2020		513		$	145.05		124,947	8.4
Total		1,157		$	139.48	$	288,265	6.0

Stock options outstanding as of December 31, 2020 are comprised of the following range of exercise prices per share (in thousands, except per share data and years):

	Stock Options Outstanding at December 31, 2020
			Weighted Average		Weighted Average
			Exercise Price		Remaining Contractual
Range of Exercise Prices per Share	Shares		Per Share		Term (Years)
$121.43 - $140.00		710	$	124.45		4.8
$140.01 - $160.00		268	$	151.33		9.0
$160.01 - $180.00		69	$	169.37		6.8
$180.01 - $201.25		110	$	188.97		6.0
Total		1,157	$	139.48		6.0

An aggregate of 200,000, 216,250, and 251,250 stock options with an aggregate fair value of $11.2 million, $12.6 million, and $15.5 million vested during the years ended December 31, 2020, 2019, and 2018, respectively.

The weighted average grant date fair value of stock option awards using the Black-Scholes option pricing model was $49.68, $54.36, and $51.68 for each share subject to a stock option granted during the years ended December 31, 2020, 2019, and 2018, respectively, based on the following assumptions:

The Company recognized approximately $10.1 million, $10.1 million, and $14.6 million in share-based compensation expense for the years ended December 31, 2020, 2019, and 2018, respectively, from stock options granted under the 2013 Equity Plan. As of December 31, 2020, there was approximately $21.8 million of total unrecognized share-based compensation expense related to unvested stock options. As of December 31, 2020, the Company expects to recognize this remaining share-based compensation expense over a weighted average vesting period of approximately 2.6 years.

During the fourth quarter of 2020, the Company began granting restricted stock units under the 2013 Equity Plan. The restricted stock units entitle recipients to receive a number of shares of the Company’s class A common stock over a vesting period, as specified in the applicable restricted stock unit agreement. Although the Company may in its sole discretion elect to pay fully or partially in cash in lieu of settling solely in shares, it does not currently intend to do so.

Share-based compensation expense related to restricted stock units is based on the fair value of the Company’s class A common stock on the date of grant. The Company recognizes share-based compensation expense associated with such restricted stock unit awards on a straight-line basis over the award’s requisite service period (generally, the vesting period). The restricted stock unit awards granted to date vest in equal annual installments over a four-year period (unless accelerated in connection with a change in control event under specified conditions as set forth in the applicable restricted stock unit agreement or otherwise in accordance with provisions of the 2013 Equity Plan or applicable restricted stock unit agreement).

As of December 31, 2020, there were 74,400 restricted stock units outstanding under the 2013 Equity Plan. The following table summarizes the Company’s restricted stock unit activity (in thousands) for the periods indicated:

	Restricted Stock Units Outstanding
				Aggregate
				Intrinsic
	Units			Value
Balance as of January 1, 2020		0
Granted		76
Vested		0		$	0
Forfeited		(2	)
Balance as of December 31, 2020		74
Expected to vest as of December 31, 2020		74		$	28,908

No restricted stock units vested during the year ended December 31, 2020. The weighted average grant date fair value of restricted stock units granted during the year ended December 31, 2020 was $192.43 based on the fair value of the Company’s class A common stock. The Company recognized approximately $0.5 million in share-based compensation expense for the year ended December 31, 2020 from restricted stock units granted under the 2013 Equity Plan. As of December 31, 2020, there was approximately $13.8 million of total unrecognized share-based compensation expense related to unvested restricted stock units. As of December 31, 2020, the Company expects to recognize this remaining share-based compensation expense over a weighted average vesting period of approximately 3.9 years.

During 2018, the Company granted certain awards characterized as “other stock-based awards” under the 2013 Equity Plan. These other stock-based awards are similar to stock options, except these awards are settled in cash only and not in shares of the Company’s class A common stock. These awards are classified as liabilities in the Company’s Consolidated Balance Sheets due to the required cash settlement feature and the fair value of the awards is remeasured each quarterly reporting period. Other stock-based awards were not granted in 2020 or 2019.

The Company recognized approximately $0.6 million in share-based compensation expense for the year ended December 31, 2020 from other stock-based awards. For the years ended December 31, 2019 and 2018, the Company did not recognize a material amount in share-based compensation expense from other stock-based awards. As of December 31, 2020, there was approximately $1.0 million of total unrecognized share-based compensation expense related to other stock-based awards. The Company expects to recognize this remaining share-based compensation expense over a weighted average vesting period of approximately 1.4 years, subject to additional fair value adjustments through the earlier of settlement or expiration.