The weighted average assumptions used to determine the share-based compensation expense for stock options using the Black-Scholes option pricing model were as follows:
| 2017 | 2016 | 2015 | ||||||||||
| Dividend yield | — | % | — | % | — | % | ||||||
| Expected volatility | 24.6 | % | 24.6 | % | 24.6 | % | ||||||
| Risk-free interest rate | 1.83 | % | 1.83 | % | 1.81 | % | ||||||
| Expected life (years) | 10 | 10 | 10 | |||||||||