Table:
|  | 2019 | 2018 | 2017 |
| --- | --- | --- | --- |
| Number of units granted | 70,543 | 56,829 | 100,958 |
| Weighted average fair value on grant date(1) (3) | $ 57.53 | $ 43.40 | $ 44.24 |
| Expected Price volatility(2) | 22.86% | 22.00% | 25.31 % |
| Risk-free interest rate(2) | 2.36% | 2.00% | 1.56 % |
Paragraphs:
PSUs – Total Shareholder Return (TSR)
The PSUs granted based on TSR are contingently awarded and will be payable in shares of the Company’s common stock subject to the condition that the number of PSUs, if any, earned by the employees upon the expiration of a three-year award performance period is dependent on the Company’s TSR ranking relative to a peer group of companies. The fair value of the PSUs based on TSR was estimated on the grant date using a Monte Carlo Simulation. Other assumptions include the expected volatility of all companies included in the TSR, the historical share price returns analysis of all companies included in the TSR and assumes dividends are reinvested. The expected volatility was based on the historical volatility for a period of time that approximates the duration between the valuation date and the end of the performance period. The risk-free interest rate is based on the Zero-Coupon Treasury STRIP yield curve matching the term from the valuation date to the end of the performance period. Compensation expense for the PSUs based on TSR (which is considered a market condition) is a fixed amount determined at the grant date fair value and is recognized 100% over the three-year award performance period regardless of whether PSUs are awarded at the end of the award performance period.
The number of PSUs granted based on TSR and the assumptions used to calculate the grant date fair value of the PSUs based on TSR are shown in the following table:
(1) For 2019, this represents the weighted average fair value for PSU awards approved during the first and third quarter.
(2) For 2019, values represent weighted average assumptions for PSU awards approved during the first and third quarter.
(3) On May 18, 2017, the O&C Committee approved a change in the vesting policy regarding the existing 2017 Three year PSU Awards for Ilham Kadri. The modified vesting terms resulted in award modification accounting treatment. The weighted average fair value on grant date reflects the impact of the fair value on date of modification for these awards.
Question:
How was the fair value of the PSUs based on TSR estimated?
Answer: a Monte Carlo Simulation