fidelity national information services , inc . and subsidiaries notes to consolidated financial statements - ( continued ) ( a ) intrinsic value is based on a closing stock price as of december 31 , 2016 of $ 75.64 . the weighted average fair value of options granted during the years ended december 31 , 2016 , 2015 and 2014 was estimated to be $ 9.35 , $ 10.67 and $ 9.15 , respectively , using the black-scholes option pricing model with the assumptions below: .

2016: risk free interest rate: -1.2
volatility: -20.4
dividend yield: -1.6
weighted average expected life ( years ): 4.2
2015: risk free interest rate: -1.4
volatility: -21.7
dividend yield: -1.6
weighted average expected life ( years ): 4.2
2014: risk free interest rate: -1.4
volatility: -21.2
dividend yield: -1.6
weighted average expected life ( years ): 4.2

the company estimates future forfeitures at the time of grant and revises those estimates in subsequent periods if actual forfeitures differ from those estimates . the company bases the risk-free interest rate that is used in the stock option valuation model on u.s . n treasury securities issued with maturities similar to the expected term of the options . the expected stock volatility factor is determined using historical daily price changes of the company's common stock over the most recent period commensurate with the expected term of the option and the impact of any expected trends . the dividend yield assumption is based on the current dividend yield at the grant tt date or management's forecasted expectations . the expected life assumption is determined by calculating the average term from the tt company's historical stock option activity and considering the impact of expected future trends . the company granted a total of 1 million restricted stock shares at prices ranging from $ 56.44 to $ 79.41 on various dates in 2016 . the company granted a total of 1 million restricted stock shares at prices ranging from $ 61.33 to $ 69.33 on various dates in 20t 15 . the company granted a total of 1 million restricted stock shares at prices ranging from $ 52.85 to $ 64.04 on various dates in 2014 . these shares were granted at the closing market price on the date of grant and vest annually over three years . as of december 31 , 2016 and 2015 , we have approximately 3 million and 4 million unvested restricted shares remaining . the december 31 , 2016 balance includes those rsu's converted in connection with the sungard acquisition as noted above . the company has provided for total stock compensation expense of $ 137 million , $ 98 million and $ 56 million for the years ended december 31 , 2016 , 2015 and 2014 , respectively , which is included in selling , general , and administrative expense in the consolidated statements of earnings , unless the expense is attributable to a discontinued operation . of the total stock compensation expense , $ 2 million for 2014 relates to liability based awards that will not be credited to additional paid in capital until issued . total d compensation expense for 2016 and 2015 did not include amounts relating to liability based awards . as of december 31 , 2016 and 2015 , the total unrecognized compensation cost related to non-vested stock awards is $ 141 million and $ 206 million , respectively , which is expected to be recognized in pre-tax income over a weighted average period of 1.4 years and 1.6 years , respectively . german pension plans our german operations have unfunded , defined benefit plan obligations . these obligations relate to benefits to be paid to germanaa employees upon retirement . the accumulated benefit obligation as of december 31 , 2016 and 2015 , was $ 49 million and $ 48 million , respectively , and the projected benefit obligation was $ 50 million and $ 49 million , respectively . the plan remains unfunded as of december 31 , 2016 . ( 15 ) divestitures and discontinued operations on december 7 , 2016 , the company entered into a definitive agreement to sell the sungard public sector and education ( "ps&e" ) businesses for $ 850 million . the transaction included all ps&e solutions , which provide a comprehensive set of technology solutions to address public safety and public administration needs of government entities as well asn the needs of k-12 school districts . the divestiture is consistent with our strategy to serve the financial services markets . we received cash proceeds , net of taxes and transaction-related expenses of approximately $ 500 million . net cash proceeds are expected to be used to reduce outstanding debt ( see note 10 ) . the ps&e businesses are included in the corporate and other segment . the transaction closed on february 1 , 2017 , resulting in an expected pre-tax gain ranging from $ 85 million to $ 90 million that will .

Questions:
what was the fair value of options at the end of 2016?
what was the fair value of options at the end of 2015?
what was the change in value from 2015 to 2016?
what was the fair value of options at the end of 2015?
what is the percent change?

Answers:
9.35
10.67
-1.32
10.67
-12.4%