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Share-Based Compensation
9 Months Ended
Sep. 30, 2020
Share-based Payment Arrangement [Abstract]  
Share-Based Compensation SHARE-BASED COMPENSATION 
The fair value of options, restricted stock units, deferred stock units, and employee stock purchase rights awarded during the three and nine months ended September 30, 2020, totaled $1.3 million and $39.9 million as compared to $3.8 million and $40.1 million for the three and nine months ended September 30, 2019. The total unrecognized compensation expense, net of estimated forfeitures, for unvested share-based compensation awards outstanding at September 30, 2020, was $64.0 million, which will be recognized over a weighted average period of approximately 1.7 years. During the three and nine months ended September 30, 2020, we recognized expenses of $7.9 million and $23.0 million as compared to $9.4 million and $22.6 million for the three and nine months ended September 30, 2019, related to share-based compensation.

We determine the assumptions used in the valuation of option awards as of the date of grant. Differences in the expected stock price volatility, expected term or risk-free interest rate may necessitate distinct valuation assumptions at each grant date. As such, we may use different assumptions for options granted throughout the year. Option awards are granted with an exercise price equal to the closing market price of our common stock at the date of grant. We have never paid any cash dividends on our common stock, and we have no intention to pay such a dividend at this time; therefore, we assume that no dividends will be paid over the expected terms of option awards.

The weighted averages of the valuation assumptions used to determine the fair value of each option award on the date of grant and the weighted average estimated fair values were as follows:
For the Nine Months Ended
September 30,
20202019
  
Share price at grant$290.15 $213.35 
Expected stock price volatility27 %26 %
Expected term, in years6.06.0
Risk-free interest rate1.4 %2.4 %
Weighted average fair value of options granted$84.60 $64.99