
	Three months ended September 30,				Nine months ended September 30,
Stock-based compensation expense:	2022		2021		2022		2021
Restricted stock and restricted stock units (1)	$	14.6	$	5.3	$	36.6	$	12.9
Stock options	3.3		1.0		4.9		2.1
Incentive units (2)	—		2.7		2.4		8.7
Total compensation expense	$	17.9	$	9.0	$	43.9	$	23.7

Expected tax benefit:
Restricted stock and restricted stock units	$	1.6	$	(0.9)	$	4.7	$	2.2
Stock options	0.3		0.1		0.4		(0.2)
Total expected tax benefit	$	1.9	$	(0.8)	$	5.1	$	2.0

(1)Higher expense for restricted stock and restricted stock units was primarily due to the addition of our 2022 grants and the expense recognition associated with accelerated shares.


Date	Number of shares granted	Weighted average grant date fair value per share	Vesting period (in years)	Vesting criteria
Restricted Stock & RSU's: (1)
March 10, 2022	96,509	$16.58	1.0	Service
March 10, 2022 (2)	3,254,916	$16.58	3.0	Service & Performance
March 31, 2022	89,334	$17.52	3.0	Service
June 30, 2022	143,052	$15.03	3.0	Service
August 5, 2022 (2)	1,998,118	$15.89	3.0	Service & Performance
September 30, 2022	176,361	$12.39	3.0	Service

Stock Options:
August 5, 2022 (3)	4,914,868	$5.42	3.0	Service & Market

(3)Awards vest ratably over three years and become exercisable when D&B's share price exceeds and remains above a target price for a period of time as defined in the grant agreements. These are market condition options. See below for further discussion.

We accounted for stock-based compensation based on grant date fair value. For restricted stock, grant date fair value was based on the closing price of our stock on the date of grant. Service condition options were valued using the Black-Scholes valuation model. Market condition options were valued using a Monte Carlo valuation model.

On August 5, 2022, we granted to certain executives 4,914,868 stock options that contained both a service condition and a market condition. The stock options have a ten-year term and will vest ratably over three years, commencing on the first anniversary of the grant date. The executives must remain continuously employed through the latter of (1) the vesting periods or (2) the time when the market condition is met. The market condition, which impacts the exercisability of the stock options, requires that D&B’s share price must exceed the grant date share price by 20% for 20 trading days in any 30-day trading window during the 10-year term of the award. As these awards contain a market condition, the fair value on the date of grant was calculated using a Monte Carlo simulation model with the following weighted average assumptions:


Weighted average assumptions
Weighted average expected stock price volatility	33.46	%
Weighted average expected dividend yield	1.29	%
Weighted average expected life of option (in years)	4.5
Weighted average risk-free interest rate	2.77	%
Weighted average grant date fair value	$5.42
Weighted average exercise price	$15.89

Expected stock price volatility was calculated based 50% on D&B’s historical volatility and 50% on the leverage-adjusted volatility of our peer companies. The expected dividend yield is based on our quarterly dividend divided by the three-month average stock price as of the grant date, annualized and continuously compounded. The expected term is based on the midpoint between the time of hurdle achievement and the expiration date. Risk free interest rate is based on the term-matched, zero-coupon risk-free rate from the Treasury Constant Maturity yield curve, continuously compounded.


	Restricted stock and Restricted stock units
	Number of shares	Weighted-average grant date fair value	Weighted-average remaining contractual term (in years)	Aggregate intrinsic value
Balances, January 1, 2022	2,757,839	$21.61	1.2	$56.5
Granted	5,581,929	$16.34
Forfeited	(554,590)	$18.62
Vested	(943,690)	$21.77
Balances, September 30, 2022	6,841,488	$17.51	1.4	$84.8


	Stock options
	Number of options	Weighted-average exercise price	Weighted-average remaining contractual term (in years)	Aggregate intrinsic value
Balances, January 1, 2022	6,380,000	$22.00	5.5	$—
Granted	4,914,868	$15.89
Forfeited	(200,000)	$22.00
Vested	—	$—
Balances, September 30, 2022	11,094,868	$19.29	7.0	$—


	Incentive units (1)
	Number of incentive units	Weighted-average grant date fair value	Weighted-average remaining contractual term (in years)	Aggregate intrinsic value
Balances, January 1, 2022	3,826,569	$2.95	0.2	$78.4
Distributed	(3,786,486)	$2.96
Forfeited	(13,703)	$2.59
Balances, September 30, 2022	26,380	$2.59	0.1	$0.3


Equity-based compensation:	Unrecognized compensation		Weighted-average amortization period (in years)
Restricted stock & Restricted stock units	$	90.2	2.3
Stock options	26.8		2.6
Incentive units (1)	—		0.1
Total unrecognized compensation expense	$	117.0	2.5

Under the Dun & Bradstreet Holdings, Inc. Employee Stock Purchase Plan, eligible employees are allowed to voluntarily make after-tax contributions ranging from 3% to 15% of eligible earnings. The Company contributes varying matching amounts to employees, as specified in the plan document, after a one year holding period. We recorded the associated expense of approximately $1 million and $3 million for the three and nine months ended September 30, 2022, respectively, and approximately $1 million and $4 million for the three and nine months ended September 30, 2021, respectively.