Our total stock-based compensation expense for the years ended May 31 was as follows (in millions):

We have two types of equity-based compensation: stock options and restricted stock.

STOCK OPTIONS. Under the provisions of our incentive stock plans, key employees and non-employee directors may be granted options to purchase shares of our common stock at a price not less than its fair market value on the date of grant. Vesting requirements are determined at the discretion of the Compensation Committee of our Board of Directors. Option-vesting periods range from one to four years, with 83% of our options vesting ratably over four years. Compensation expense associated with these awards is recognized on a straight-line basis over the requisite service period of the award.

RESTRICTED STOCK. Under the terms of our incentive stock plans, restricted shares of our common stock are awarded to key employees. All restrictions on the shares expire ratably over a four-year period. Shares are valued at the market price on the date of award. The terms of our restricted stock provide for continued vesting subsequent to the employee's retirement. Compensation expense associated with these awards is recognized on a straight-line basis over the shorter of the remaining service or vesting period.

VALUATION AND ASSUMPTIONS. We use the Black-Scholes option pricing model to calculate the fair value of stock options. The value of restricted stock awards is based on the stock price of the award on the grant date. We record stock-based compensation expense in the “Salaries and employee benefits” caption in the accompanying consolidated statements of income.

The key assumptions for the Black-Scholes valuation method include the expected life of the option, stock price volatility, a risk-free interest rate and dividend yield. Following is a table of the weighted-average Black-Scholes value of our stock option grants, the intrinsic value of options exercised (in millions) and the key weighted-average assumptions used in the valuation calculations for options granted during the years ended May 31, and then a discussion of our methodology for developing each of the assumptions used in the valuation model:

		2015			2014			2013
Weighted-average Black-Scholes value		$	53.33		$	35.79		$	29.20
Intrinsic value of options exercised		$	253		$	347		$	107
Black-Scholes Assumptions:
	Expected lives		6.3 years			6.2 years			6.1 years
	Expected volatility		34	%		35	%		35	%
	Risk-free interest rate		2.02	%		1.47	%		0.94	%
	Dividend yield		0.448	%		0.561	%		0.609	%

The expected life represents an estimate of the period of time options are expected to remain outstanding, and we examine actual stock option exercises to determine the expected life of the options. Options granted have a maximum term of 10 years. Expected volatilities are based on the actual changes in the market value of our stock and are calculated using daily market value changes from the date of grant over a past period equal to the expected life of the options. The risk-free interest rate is the U.S. Treasury Strip rate posted at the date of grant having a term equal to the expected life of the option. The expected dividend yield is the annual rate of dividends per share over the exercise price of the option.

The following table summarizes information about stock option activity for the year ended May 31, 2015:

		Stock Options
		Shares		Weighted-Average Exercise Price	Weighted-Average Remaining Contractual Term	Aggregate Intrinsic Value (in millions)⁽¹⁾
Outstanding at June 1, 2014		15,634,856	$	91.71
	Granted	2,445,146		150.32
	Exercised	(3,516,512)		91.18
	Forfeited	(341,666)		107.62
Outstanding at May 31, 2015		14,221,824	$	101.54	6.1	$	1,031
Exercisable		7,994,368	$	89.19	4.5	$	678
Expected to vest		5,853,809	$	117.39	8.2	$	331
Available for future grants		13,157,142

⁽¹⁾	Only presented for options with market value at May 31, 2015 in excess of the exercise price of the option.

The options granted during the year ended May 31, 2015 are primarily related to our principal annual stock option grant in June 2014.

The following table summarizes information about vested and unvested restricted stock for the year ended May 31, 2015:

		Restricted Stock
		Shares	Weighted-Average Grant Date Fair Value
Unvested at June 1, 2014		480,157	$	91.46
	Granted	154,115		148.89
	Vested	(192,920)		88.33
	Forfeited	(2,310)		116.12
Unvested at May 31, 2015		439,042	$	112.87

During the year ended May 31, 2014, there were 191,964 shares of restricted stock granted with a weighted-average fair value of $100.80. During the year ended May 31, 2013, there were 220,391 shares of restricted stock granted with a weighted-average fair value of $85.45.

The following table summarizes information about stock option vesting during the years ended May 31:

	Stock Options
	Vested during the year	Fair value (in millions)
2015	2,611,524	$	83
2014	2,408,179		65
2013	2,824,757		81

As of May 31, 2015, there was $183 million of total unrecognized compensation cost, net of estimated forfeitures, related to unvested share-based compensation arrangements. This compensation expense is expected to be recognized on a straight-line basis over the remaining weighted-average vesting period of approximately two years.

Total shares outstanding or available for grant related to equity compensation at May 31, 2015 represented 9% of the total outstanding common and equity compensation shares and equity compensation shares available for grant.