The Company has outstanding stock-based compensation awards granted under the 2013 Stock Incentive Plan (“2013 Plan”) and the 2017 Omnibus Incentive Plan (“2017 Plan”) as described in Note 17, “Stock-Based Compensation Plans” to the consolidated financial statements in its 2020 Form 10-K.

The Company’s stock-based compensation awards are typically granted in the first quarter of the year and primarily consist of stock options, restricted stock units and performance share units. Eligible employees were also granted restricted stock units, during the three months ended September 30, 2020, that vest ratably over two years, subject to the passage of time and the employee's continued employment during such period. In some instances, such as death, awards may vest concurrently with or following an employee's termination.

Stock-based compensation expense for the nine month periods ended September 30, 2021 and 2020 are included in “Cost of sales” and “Selling and administrative expenses” in the Condensed Consolidated Statements of Operations and are as follows.


	For the Three Month Period Ended September 30,				For the Nine Month Period Ended September 30,
	2021		2020		2021		2020
Stock-based compensation expense - continuing and discontinued operations	$	21.9	$	12.8	$	75.9	$	29.0
Stock-based compensation expense recognized in discontinued operations	—		0.9		10.9		1.7
Stock-based compensation expense recognized in continuing operations	$	21.9	$	11.9	$	65.0	$	27.3

In the nine month period ended September 30, 2021, the $65.0 million of stock-based compensation expense included expense for equity awards granted under the 2013 and 2017 Plan of $64.5 million and an increase in the liability for stock appreciation rights (“SAR”) of $0.5 million. Of the $64.5 million of expense for equity awards granted under the 2013 Plan and 2017 Plan, $43.1 million related to the $150 million equity grant to nearly 16,000 employees worldwide made in the third quarter of 2020 (“All-Employee Equity Grant”).

As of September 30, 2021, there was $109.1 million of total unrecognized compensation expense related to outstanding stock options, restricted stock unit awards and performance stock unit awards.

In the nine month period ended September 30, 2021, the $10.9 million of stock-based compensation expense included expense for modifications of equity awards of $3.8 million and expense for equity awards granted under the 2013 and 2017 Plan of $7.1 million. The modifications allowed for the vesting of the first tranche of the All-Employee Equity Grant awarded to HPS and SVT employees despite their termination due to the divestitures. Of the $7.1 million of expense for equity awards granted under the 2013 Plan and 2017 Plan, $5.4 million related to the All-Employee Equity Grant.

Stock options are granted to employees with an exercise price equal to the fair value of the Company’s per share common stock on the date of grant. Stock option awards typically vest over four or five years and expire ten years from the date of grant.

A summary of the Company’s stock option (including SARs) activity for the nine month period ended September 30, 2021 is presented in the following table (underlying shares in thousands).


	Shares	Weighted-Average Exercise Price (per share)
Stock options outstanding as of December 31, 2020	7,742	$	18.47

Granted	793	45.75
Exercised or settled	(1,305)	15.97
Forfeited	(231)	30.57
Expired	(6)	13.01
Stock options outstanding as of September 30, 2021	6,993	21.64

Vested as of September 30, 2021	4,551	15.85

The following assumptions were used to estimate the fair value of options granted during the nine month periods ended September 30, 2021 and 2020 using the Black-Scholes option-pricing model.


	For the Nine Month Period Ended September 30,
Assumptions	2021		2020
Expected life of options (in years)	6.3		6.3
Risk-free interest rate	0.9% - 1.1%		0.4% - 1.5%
Assumed volatility	38.9% - 39.4%		24.6% - 41.1%
Expected dividend rate	0.0	%	0.0	%

Restricted stock units are granted to employees and non-employee directors based on the market price of the Company’s common stock on the grant date and recognized in compensation expense over the vesting period. A summary of the Company’s restricted stock unit activity for the nine month period ended September 30, 2021 is presented in the following table (underlying shares in thousands).


	Shares	Weighted-Average Grant-Date Fair Value
Non-vested as of December 31, 2020	5,546	$	33.09

Granted	340	45.74
Vested	(2,497)	33.38
Forfeited	(616)	34.21
Non-vested as of September 30, 2021	2,773	34.13

Performance share units are granted to employees and are subject to a three year performance period. The number of shares issued at the end of the performance period is determined by the Company’s total shareholder return percentile rank versus the S&P 500 index for the three year performance period. The grant date fair value of these awards is determined using a Monte Carlo simulation pricing model and compensation cost is recognized straight-line over a three year period.

A summary of the Company’s performance stock unit activity for the nine month period ended September 30, 2021 is presented in the following table (underlying shares in thousands).


	Shares	Weighted-Average Grant-Date Fair Value
Non-vested as of December 31, 2020	255	$	29.72
Granted	158	55.84
Forfeited	(20)	36.36
Non-vested as of September 30, 2021	393	39.89

The following assumptions were used to estimate the fair value of performance share units granted during the nine month periods ended September 30, 2021 and 2020 using the Monte Carlo simulation pricing model.


	For the Nine Month Period Ended September 30,
Assumptions	2021		2020
Expected term (in years)	2.9		2.8
Risk-free interest rate	0.2	%	0.5	%
Assumed volatility	36.9	%	35.2	%
Expected dividend rate	—	%	—	%