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Stock compensation (Details) - USD ($) $ / shares in Units, $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Sep. 30, 2019 | Sep. 30, 2018 | Sep. 30, 2019 | Sep. 30, 2018
Stock compensation |  |  |  |
Stock compensation expense | $ 43.4 | $ 38.0 | $ 124.6 | $ 110.8
Stock Compensation Expense Capitalized | 0.1 |  | $ 0.3 |
Weighted-average fair value assumptions |  |  |  |
Valuation method |  |  | Black-Scholes valuation model |
Dividend yield (as a percent) |  |  | 0.00% |
Research and Development Expense [Member] |  |  |  |
Stock compensation |  |  |  |
Stock compensation expense | 30.5 | 26.3 | $ 85.5 | 75.3
Selling, General and Administrative Expenses [Member] |  |  |  |
Stock compensation |  |  |  |
Stock compensation expense | 12.8 | $ 11.7 | 38.6 | $ 35.5
Cost of product revenues |  |  |  |
Stock compensation |  |  |  |
Stock compensation expense | $ 0.1 |  | $ 0.5 |
Stock Options |  |  |  |
Weighted-average fair value assumptions |  |  |  |
Average risk-free interest rates (as a percent) | 1.74% | 2.72% | 2.29% | 2.60%
Average expected life (in years) | 5 years 1 month 2 days | 5 years 10 days | 5 years 3 months 10 days | 5 years 3 months 7 days
Volatility (as a percent) | 45.00% | 45.00% | 45.00% | 45.00%
Weighted-average fair value (in dollars per share) | $ 34.83 | $ 29.32 | $ 32.38 | $ 34.41
Unrecognized compensation |  |  |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 114.4 |  | $ 114.4 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards |  |  | 1 year 7 months 6 days |
Restricted Stock Units (RSUs) |  |  |  |
Weighted-average fair value assumptions |  |  |  |
Average risk-free interest rates (as a percent) | 1.63% | 2.81% | 1.94% | 2.63%
Average expected life (in years) | 6 months | 6 months | 6 months | 6 months
Volatility (as a percent) | 34.00% | 27.00% | 34.00% | 45.00%
Weighted-average fair value (in dollars per share) | $ 15.04 | $ 13.56 | $ 14.53 | $ 15.91
Unrecognized compensation |  |  |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 102.0 |  | $ 102.0 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards |  |  | 1 year 10 months 24 days |
Performance Stock Units (PSUs) |  |  |  |
Unrecognized compensation |  |  |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 34.4 |  | $ 34.4 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards |  |  | 2 years 4 months 24 days |

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- Definition The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2)(iii) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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