The following table summarizes stock-based compensation expense related to stock options, performance stock units (PSUs), restricted stock units (RSUs) and restricted stock for the three and six months ended June 30, 2019 and 2018:

	Three Months Ended						Six Months Ended
	June 30,						June 30,
(In thousands)	2019			2018			2019			2018
Stock-based compensation expense included in cost of sales	$	85		$	102		$	189		$	197
Selling, general and administrative expense		662			995			1,725			2,030
Research and development expense		707			687			1,399			1,376
Stock-based compensation expense included in operating expenses		1,369			1,682			3,124			3,406
Total stock-based compensation expense		1,454			1,784			3,313			3,603
Tax benefit for expense associated with stock options, PSUs, RSUs and restricted stock		(332	)		(340	)		(775	)		(724	)
Total stock-based compensation expense, net of tax	$	1,122		$	1,444		$	2,538		$	2,879

The following table is a summary of our stock options outstanding as of December 31, 2018 and June 30, 2019, and the changes that occurred during the six months ended June 30, 2019:

	Number of Stock Options (in thousands)			Weighted Avg. Exercise Price (per share)		Weighted Avg. Remaining Contractual Life (in years)		Aggregate Intrinsic Value (in thousands)
Stock options outstanding, December 31, 2018		4,382		$	22.91		4.10	$	—
Stock options exercised		(34	)	$	15.53
Stock options forfeited		(10	)	$	15.67
Stock options expired		(156	)	$	24.50
Stock options outstanding, June 30, 2019		4,182		$	22.93		3.64	$	—
Stock options exercisable, June 30, 2019		3,942		$	23.39		3.47	$	—

At June 30, 2019, total unrecognized compensation expense related to non-vested stock options was approximately $0.3 million, which is expected to be recognized over an average remaining recognition period of 0.4 years.

All of the options above were issued at exercise prices that approximated fair market value at the date of grant.

The aggregate intrinsic value of stock options represents the total pre-tax intrinsic value (the difference between ADTRAN’s closing stock price on the last trading day of the quarter and the exercise price, multiplied by the number of in-the-money options) that would have been received by the option holders had all option holders exercised their options on June 30, 2019. The amount of aggregate intrinsic value will change based on the fair market value of ADTRAN’s stock and was zero as of June 30, 2019. The total pre-tax intrinsic value of options exercised during the six months ended June 30, 2019 was $0.1 million.

The fair value of our stock options is estimated using the Black-Scholes model. The determination of the fair value of stock options on the date of grant using the Black-Scholes model is affected by our stock price, as well as assumptions regarding a number of complex and subjective variables that may have a significant impact on the fair value estimate. The stock option pricing model requires the use of several assumptions that impact the fair value estimate. These variables include, but are not limited to, the volatility of our stock price and employee exercise behaviors.

There were no stock options granted during the three and six months ended June 30, 2019 or 2018.

The following table is a summary of our PSUs, RSUs and restricted stock outstanding as of December 31, 2018 and June 30, 2019 and the changes that occurred during the six months ended June 30, 2019:

	Number of Shares (in thousands)			Weighted Avg. Grant Date Fair Value (per share)
Unvested PSUs, RSUs and restricted stock outstanding, December 31, 2018		1,570		$	18.52
PSUs, RSUs and restricted stock granted		59		$	12.54
PSUs, RSUs and restricted stock vested		(1	)	$	18.86
PSUs, RSUs and restricted stock forfeited		(63	)	$	16.66
Unvested PSUs, RSUs and restricted stock outstanding, June 30, 2019		1,565		$	18.37

The fair value of our PSUs with market and performance conditions is calculated using a Monte Carlo simulation valuation method. The fair value of RSUs and restricted stock is equal to the closing price of our stock on the business day immediately preceding the grant date.

At June 30, 2019, total unrecognized compensation expense related to the non-vested portion of market-based PSUs, RSUs and restricted stock was approximately $14.2 million, which is expected to be recognized over an average remaining recognition period of 2.6 years. In addition, there was $8.3 million of unrecognized compensation expense related to unvested 2017 performance-based PSUs, which will be recognized over the remaining requisite service period of 0.5 years if achievement of the performance obligation becomes probable. For the three and six months ending June 30, 2019 and 2018, no compensation expense was recognized related to these 2017 performance-based PSUs.

At June 30, 2019, 2.6 million stock options, PSUs, RSUs or restricted stock were available for grant under shareholder-approved equity plans.