Share-based Compensation

Pursuant to 2015 Management Incentive Plan as described in Note 16 "Capital Structure", and in connection with the IPO, non-qualified stock options to purchase shares of Class A common stock were granted, each of which vests in equal annual installments over a period of the four years from grant date and expires not later than 10 years from the date of grant.

The following table summarizes activity related to stock options for the nine months ended September 30, 2018 and 2017:



	Options Outstanding					Options Exercisable
	Number of Options		Weighted Average Exercise Price Per Share		Weighted Average Remaining Contractual Life	Number of Options		Weighted Average Exercise Price Per Share
At December 31, 2016	8,234,000		$	19.00	8.29	2,058,500		$	19.00
Granted	—		—		—	—		—
Exercised	—		—		—	—		—
Forfeited or expired	(401,000	)	—		—	—		—
At September 30, 2017	7,833,000		$	19.00	7.55	3,916,500		$	19.00

At December 31, 2017	7,783,000		$	19.00	7.29	3,891,500		$	19.00
Granted	—		—		—	—		—
Exercised	(4,086,558	)	19.00		—	(4,086,558	)	19.00
Forfeited or expired	(83,750	)	—		—	—		—
At September 30, 2018	3,612,692		$	19.00	6.55	1,741,942		$	19.00

The expected life has been determined based on an average of vesting and contractual period. The risk-free interest rate was determined based on the yields available on U.S. Treasury zero-coupon issues. The expected stock price volatility was determined based on historical volatilities of comparable companies. The expected dividend yield was determined based on estimated future dividend payments divided by the IPO stock price.

The Company recognized $1.4 million and $1.4 million for the three months ended September 30, 2018, and 2017, respectively, and $4.2 million and $4.2 million for the nine months ended September 30, 2018, and 2017, respectively, of compensation expense in relation to the stock options issued and outstanding. As of September 30, 2018 and December 31, 2017, total unrecognized share-based compensation expense related to unvested stock options was $3.1 million and $7.5 million, respectively, and these amounts are to be recognized over a weighted average period of 0.6 and 1.3 years, respectively.

Class A common stock and Restricted Stock Units

Pursuant to the 2015 Management Incentive Plan as described in Note 16 "Capital Structure", subsequent to the IPO, shares of immediately vested Class A common stock and restricted stock units were granted, the latter which vest over a period of up to 4 years. The fair value of the Class A common stock and RSUs was determined based on a volume weighted average price and is being recognized on a straight line basis over the vesting period. For the nine months ended September 30, 2018, there were 594,536 shares of immediately vested Class A common stock granted as part of 2017 year-end compensation, with a fair value of $11.3 million which was recorded as an increase to the condensed consolidated statements of changes in equity. In addition, the Company accrued compensation expense of $2.5 million and $0.0 million for the three months ended September 30, 2018 and 2017, respectively, and $7.1 million and $9.4 million for the nine months ended September 30, 2018 and 2017, respectively, related to immediately vested Class A common stock expected to be awarded as part of year-end incentive compensation, which was included in employee compensation and payroll taxes on the condensed consolidated statements of comprehensive income and accounts payable and accrued expenses and other liabilities on the condensed consolidated statements of financial condition.

The following table summarizes activity related to the RSUs:



	Number of Shares		Weighted Average Fair Value
At December 31, 2016	1,573,441		$	18.28
Granted	34,825		17.95
Forfeited	(212,729	)	18.46
Vested	(58,536	)	19.22
At September 30, 2017	1,337,001		18.21

At December 31, 2017	853,047		17.94
Granted	1,265,899		20.89
Forfeited	(127,493	)	18.30
Vested	(83,942	)	18.25
At September 30, 2018	1,907,511		$	19.86

The Company recognized $4.6 million and $2.2 million for the three months ended September 30, 2018 and 2017, respectively, and $13.1 million and $7.1 million for the nine months ended September 30, 2018 and 2017, respectively, of compensation expense in relation to the restricted stock units. As of September 30, 2018 and December 31, 2017, total unrecognized share-based compensation expense related to unvested RSUs was $25.0 million and $14.3 million, respectively, and this amount is to be recognized over a weighted average period of 1.1 and 1.5 years, respectively.