Weighted average period

[Table of Contents](#ie5b53d08516744208c4d15ed88453ce2_7)Stock OptionsWe did not grant any stock options in the year ended December 31, 2021. For the years ended December 31, 2020 and 2019, the fair value of each stock option granted under our plans was estimated on the date of grant using the Black-Scholes option pricing model with the following assumptions:  

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
|  |  |  | Year Ended December 31 |
|  |  |  | 2020 |  | 2019 |
| Expected term (in years)  |  |  | 5.0 |  | 6.9 |
| Risk-free interest rate  |  |  | 0.4  | % |  | 2.5  | % |
| Expected volatility  |  |  | 43.5  | % |  | 42.8  | % |
| Dividend rate  |  |  | —  | % |  | —  | % |

ESPPThe following table summarizes the assumptions relating to our ESPP:

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
|  |  | Year Ended December 31, |
|  |  | 2021 |  | 2020 |  | 2019 |
| Expected term (in years)  |  | 1.2 |  | 1.6 |  | 1.1 |
| Risk-free interest rate  |  | 0.1  | % |  | 0.4  | % |  | 1.8  | % |
| Expected volatility  |  | 40.2  | % |  | 45.1  | % |  | 42.5  | % |
| Dividend rate  |  | —  | % |  | —  | % |  | —  | % |

As of December 31, 2021, there were $519.7 million of unrecognized compensation costs related to all unvested awards. The unamortized compensation costs are expected to be recognized over a weighted-average period of approximately 3.3 years.   
  
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