235/264 Notes to the 2017 consolidated financial statements The weighted­average contractual life for the share options outstanding at December 31, 2015, 2016, and 2017 is 2.5 years, 3.4 years, and 3.3 years, respectively. The weighted­average share price at exercise for options exercised during 2015, 2016, and 2017 was US$43.60, US$42.05, and US$57.53, respectively. The weighted­average fair value of options granted during the year ended December 31, 2015, 2016, and 2017 was US$15.58 per option, US$13.10 per option, and US$18.05 per option, respectively. The share options outstanding are comprised of the following: 2015 2016 2017 Number of options Weighted average remaining contractual life (years) Number of options Weighted average remaining contractual life (years) Number of options Weighted average remaining contractual life (years) Range of exercise prices (US$) Below 40.00 6,610,400 1.9 2,731,080 2.0 1,545,440 1.4 40.00 – 42.50 1,268,160 4.3 6,320,120 4.0 5,734,920 2.7 Above 42.50 1,313,560 4.3 1,925,280 3.6 7,366,360 3.8 9,192,120 2.5 10,976,480 3.4 14,646,720 3.3 In determining the fair value of the employee share­based awards, the Group uses the Black­Scholes option­pricing model. The Company does not anticipate paying any cash dividends in the near future and therefore uses an expected dividend yield of zero in the option valuation model. The expected volatility is based on the historical volatility of public companies that are comparable to the Group over the expected term of the award. The risk­free rate is based on U.S. Treasury zero­coupon rates as the exercise price is based on a fixed USD amount. The expected life of the share options is based on historical data and current expectations. The following table lists the inputs to the Black­Scholes option­pricing models used for employee share­based payments for the years ended December 31, 2015, 2016, and 2017: 2015 2016 2017 Expected volatility (%) 39.4 – 55.9 37.9 – 45.8 32.0 – 43.5 Risk­free interest rate (%) 0.9 – 1.6 0.8 – 1.8 1.4 – 2.0 Expected life of share options (years) 2.8 – 5.2 2.5 – 5.0 2.4 – 4.4 Weighted­average share price (US$) 36.20 – 46.50 41.20 – 44.40 50.70 – 90.65 Valuation assumptions are determined at each grant date and, as a result, are likely to change for share­based awards granted in future periods. Changes to the input assumptions could materially affect the estimated fair value of share­based payment awards. F­42