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Stock compensation (Details) - USD ($) $ / shares in Units, $ in Millions | 3 Months Ended | 6 Months Ended
--- | --- | ---
Jun. 30, 2020 | Jun. 30, 2019 | Jun. 30, 2020 | Jun. 30, 2019
Stock compensation |  |  |  |
Stock compensation expense | $ 46.3 | $ 40.6 | $ 88.8 | $ 81.2
Stock Compensation Expense Capitalized | 0.1 | 0.1 | $ 0.3 | 0.2
Assumed annualized forfeiture rate (as a percent) |  |  | 5.00% |
Weighted-average fair value assumptions |  |  |  |
Valuation method |  |  | Black-Scholes valuation model |
Research and Development Expense |  |  |  |
Stock compensation |  |  |  |
Stock compensation expense | 32.5 | 27.6 | $ 61.2 | 55.0
Selling, General and Administrative Expenses |  |  |  |
Stock compensation |  |  |  |
Stock compensation expense | 13.6 | 12.8 | 27.1 | 25.8
Cost of product revenues |  |  |  |
Stock compensation |  |  |  |
Stock compensation expense | $ 0.2 | $ 0.2 | $ 0.5 | $ 0.4
Stock Options |  |  |  |
Weighted-average fair value assumptions |  |  |  |
Average risk-free interest rates (as a percent) | 0.33% | 2.26% | 1.32% | 2.49%
Average expected life (in years) | 5 years 5 months 23 days | 5 years 6 months 18 days | 4 years 9 months 18 days | 5 years 4 months 2 days
Volatility (as a percent) | 39.00% | 39.00% | 40.00% | 45.00%
Weighted-average fair value (in dollars per share) | $ 34.13 | $ 30.92 | $ 29.49 | $ 31.47
Unrecognized compensation |  |  |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 79.9 |  | $ 79.9 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards |  |  | 1 year 3 months 18 days |
Restricted Stock Units (RSUs) |  |  |  |
Weighted-average fair value assumptions |  |  |  |
Average risk-free interest rates (as a percent) | 0.16% | 1.75% | 0.19% | 2.10%
Average expected life (in years) | 6 months | 6 months | 6 months | 6 months
Volatility (as a percent) | 38.00% | 37.00% | 48.00% | 34.00%
Weighted-average fair value (in dollars per share) | $ 19.50 | $ 13.11 | $ 17.47 | $ 13.69
Unrecognized compensation |  |  |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 77.9 |  | $ 77.9 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards |  |  | 1 year 7 months 6 days |
Performance Stock Units (PSUs) |  |  |  |
Unrecognized compensation |  |  |  |
Unrecognized compensation cost for nonvested option (in dollars) | $ 21.4 |  | $ 21.4 |
Vesting period of recognition of the unrecognized compensation cost of nonvested awards |  |  | 1 year 6 months |

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- Definition The estimated measure of the percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period. + 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)(ii) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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