86 UNITED TECHNOLOGIES CORPORATION nized in operating results. The associated future income tax benefit recognized was $76 million, $75 million and $47 million for the years ended December 31, 2012, 2011 and 2010, respectively. For the years ended December 31, 2012, 2011 and 2010, the amount of cash received from the exercise of stock options was $381 million, $226 million and $386 million, respectively, with an associated tax benefit realized of $111 million, $101 million and $139 million, respectively. In addition, for the years ended December 31, 2012, 2011 and 2010, the associated tax benefit realized from the vesting of performance share units was $15 mil- lion, $19 million and $20 million, respectively. Also, in accordance with the Compensation—Stock Compensation Topic of the FASB ASC, for the years ended December 31, 2012, 2011 and 2010, $67 million, $81 million and $94 million, respectively, of certain tax bene- fits have been reported as operating cash outflows with corresponding cash inflows from financing activities. At December 31, 2012, there was $185 million of total unrecognized compensation cost related to non-vested equity awards granted under long-term incentive plans. This cost is expected to be recognized ratably over a weighted-average period of 1.9 years. A summary of the transactions under all long-term incentive plans for the year ended December 31, 2012 follows: * weighted-average exercise price ** weighted-average grant stock price The weighted-average grant date fair value of stock options and stock appreciation rights granted during 2012, 2011 and 2010 was $19.32, $20.26 and $17.86, respectively. The weighted- average grant date fair value of performance share units, which vest upon achieving certain performance metrics, granted during 2012, 2011, and 2010 was $82.15, $87.65 and $78.73, respectively. The total fair value of awards vested during the years ended December 31, 2012, 2011 and 2010 was $187 million, $170 million and $172 million, respectively. The total intrinsic value (which is the amount by which the stock price exceeded the exercise price on the date of exercise) of stock options and stock appreciation rights * weighted-average exercise price per share ** weighted-average contractual remaining term in years The fair value of each option award is estimated on the date of grant using a binomial lattice model. The following table indicates the assumptions used in estimating fair value for the years ended December 31, 2012, 2011 and 2010. Lattice-based option models incorporate ranges of assumptions for inputs, those ranges are as follows: exercised during the years ended December 31, 2012, 2011 and 2010 was $370 million, $336 million and $446 million, respectively. The total intrinsic value (which is the stock price at vesting) of per- formance share units vested was $46 million, $59 million and $62 million during the years ended December 31, 2012, 2011 and 2010, respectively. The following table summarizes information about equity awards outstanding that are vested and expected to vest and equity awards outstanding that are exercisable at December 31, 2012: 2012 2011 2010 Expected volatility 30% – 35% 26% – 32% 24% – 28% Weighted-average volatility 30% 26% 25% Expected term (in years) 7.4 – 7.7 7.5 – 8.0 7.4 – 7.9 Expected dividends 2.3% 2.4% 2.7% Risk-free rate 0.0% – 2.0% 0.1% – 3.5% 0.1% – 4.0% Equity Awards Vested and Expected to Vest Equity Awards That Are Exercisable (SHARES IN THOUSANDS, AGGREGATE INTRINSIC VALUE IN MILLIONS) Awards Average Price* Aggregate Intrinsic Value Remaining Term** Awards Average Price* Aggregate Intrinsic Value Remaining Term** Stock Options/Stock Appreciation Rights 51,737 $ 63.90 $ 937 5.2 35,142 $ 58.44 $ 828 3.7 Performance Share Units/Restricted Stock 3,645 – 299 1.2 Stock Options Stock Appreciation Rights Performance Share Units Other Incentive Shares / Units (SHARES AND UNITS IN THOUSANDS) Shares Average Price* Shares Average Price* Units Average Price** Outstanding at: December 31, 2011 21,029 $ 47.63 34,038 $ 66.70 2,962 $ 67.31 1,109 Granted 428 75.47 7,909 74.88 1,159 74.71 467 Exercised/earned (7,546) 40.36 (2,645) 60.70 (607) 55.82 (207) Cancelled (105) 50.93 (881) 70.88 (723) 60.03 (85) December 31, 2012 13,806 $ 52.45 38,421 $ 68.70 2,791 $ 74.77 1,284