Stock Options  MINERALS TECHNOLOGIES INC. AND SUBSIDIARY COMPANIES  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS  The fair value of options granted is estimated on the date of grant using the Black-Scholes valuation model. Compensation expense is recognized only for those options expected to vest, with forfeitures estimated at the date of grant  based on the Company's historical experience and future expectations. The forfeiture rate assumption used for the periods  ended December 31, 2013 and 2012 was 7.50% and 7.31%, respectively.  The weighted average grant date fair value for stock options granted during the years ended December 31, 2013, 2012 and  2011 was $15.83, $10.74 and $11.03, respectively. The weighted average grant date fair value for stock options vested during  2013, 2012 and 2011 was $10.29, $8.57 and $7.58, respectively. The total intrinsic value of stock options exercised during  the years ended December 31, 2013, 2012 and 2011 was $10.0 million, $3.3 million and $1.7 million, respectively.  The fair value for stock awards was estimated at the date of grant using the Black-Scholes option valuation model with  the following weighted average assumptions for the years ended December 31, 2013, 2012 and 2011:  The expected term of the options represents the estimated period of time until exercise and is based on historical  experience of similar awards, based upon contractual terms, vesting schedules, and expectations of future employee behavior. The expected stock-price volatility is based upon the historical and implied volatility of the Company's stock. The interest  rate is based upon the implied yield on U.S. Treasury bills with an equivalent remaining term. Estimated dividend yield is  based upon historical dividends paid by the Company.  The following table summarizes stock option activity for the year ended December 31, 2013:  The aggregate intrinsic value above is calculated before applicable income taxes, based on the Company's closing stock  price of $60.07 as of the last business day of the period ended December 31, 2013 had all options been exercised on that date.  The weighted average intrinsic value of the options exercised during 2013, 2012 and 2011 was $20.03, $10.11 and $7.15 per  share, respectively. As of December 31, 2013, total unrecognized stock-based compensation expense related to non-vested  stock options was approximately $2.4 million, which is expected to be recognized over a weighted average period of  approximately three years.  The Company issues new shares of common stock upon the exercise of stock options.  F-11  Shares  Weighted  Average  Exercise  Price Per  Share  Weighted  Average  Remaining  Contractual  Life (Years)  Aggregate  Intrinsic Value (in thousands)  Balance December 31, 2012 ........................  1,395,520  $  28.31  Granted ........................................................ 239,770 41.42  Exercised ..................................................... (501,222) 25.26  Canceled ...................................................... (2,653 )  37.24  Balance December 31, 2013 ........................  1,131,415  $  32.42  6.16  $ 31,283 Exercisable, December 31, 2013 ................. 758,014 $  29.67  4.95  $ 23,046 2013  2012  2011  Expected life (years)...................................... 6.9  6.9  6.3 Interest rate .................................................... 1.22%  1.36% 2.46 %  Volatility ........................................................ 37.82%  31.26% 30.93 %  Expected dividend yield ................................ 0.48%  0.31% 0.31 % 