22.  STOCK‑BASED COMPENSATION PLAN

Under the 2016 Stock Incentive Plan, we may grant nonqualified stock options, incentive stock options, stock appreciation rights, restricted stock, phantom stock, performance share units and other stock-based awards to our employees, directors and consultants and to employees and consultants of our subsidiaries, provided that incentive stock options may be granted solely to employees. The terms of the grants under both the 2016 Stock Incentive Plan and the Prior Plan are fixed at the grant date. Initially, there were approximately 8.2 million shares available for issuance under the 2016 Stock Incentive Plan. However, the number of shares available for issuance may be adjusted to include any shares surrendered, exchanged, forfeited or settled in cash pursuant to the Prior Plan. As of December 31, 2018, we had approximately 9.5 million shares remaining under the 2016 Stock Incentive Plan available for grant. Option awards have a maximum contractual term of 10 years and generally must have an exercise price at least equal to the market price of our common stock on the date the option award is granted. Outstanding stock-based awards generally vest over a three‑year period.

 

The compensation cost under the 2016 Stock Incentive Plan and the Prior Plan for our Company and Huntsman International were as follows (dollars in millions):

 

The total income tax benefit recognized in the statement of operations for stock-based compensation arrangements was $18 million,  $18 million and $7 million for the years ended December 31, 2018, 2017 and 2016, respectively.

Stock Options

The fair value of each stock option award is estimated on the date of grant using the Black-Scholes valuation model that uses the assumptions noted in the following table. Expected volatilities are based on the historical volatility of our common stock through the grant date. The expected term of options granted was estimated based on the contractual term of the instruments and employees’ expected exercise and post‑vesting employment termination behavior. The risk‑free rate for periods within the contractual life of the option was based on the U.S. Treasury yield curve in effect at the time of grant. The assumptions noted below represent the weighted averages of the assumptions utilized for all stock options granted during the year.

 

A summary of stock option activity under the 2016 Stock Incentive Plan and the Prior Plan as of December 31, 2018 and changes during the year then ended is presented below:

 

The weighted‑average grant‑date fair value of stock options granted during 2018, 2017 and 2016 was $15.20,  $9.26 and $3.15 per option, respectively. As of December 31, 2018, there was $8 million of total unrecognized compensation cost related to nonvested stock option arrangements granted under the 2016 Stock Incentive Plan and the Prior Plan. That cost is expected to be recognized over a weighted-average period of approximately 1.8 years.

During the years ended December 31, 2018, 2017 and 2016, the total intrinsic value of stock options exercised was approximately $78 million, $48 million and $1 million, respectively. Cash received from stock options exercised during the years ended December 31, 2018, 2017 and 2016 was approximately $17 million, $35 million and $1 million, respectively. The cash tax benefit from stock options exercised during the years ended December 31, 2018, 2017 and 2016 was approximately $17 million, $15 million, and nil, respectively.

Nonvested Shares

Nonvested shares granted under the 2016 Stock Incentive Plan and the Prior Plan consist of restricted stock and performance share unit awards, which are accounted for as equity awards, and phantom stock, which is accounted for as a liability award because it can be settled in either stock or cash.

The fair value of each performance share unit award is estimated using a Monte Carlo simulation model that uses various assumptions, including an expected volatility rate and a risk-free interest rate. For the years ended December 31, 2018, 2017 and 2016, the weighted-average expected volatility rate was 44.3%.  45.0% and 39.3%, respectively, and the weighted average risk-free interest rate was 2.3%,  1.5% and 0.9%, respectively. For the performance share unit awards granted during the years ended December 31, 2018, 2017 and 2016, the number of shares earned varies based upon the Company achieving certain performance criteria over a three-year performance period. The performance criteria are total stockholder return of our common stock relative to the total stockholder return of a specified industry peer group for the three-year performance periods.

A summary of the status of our nonvested shares as of December 31, 2018 and changes during the year then ended is presented below:

As of December 31, 2018, there was $19 million of total unrecognized compensation cost related to nonvested share compensation arrangements granted under the Stock Incentive Plan and the Prior Plan. That cost is expected to be recognized over a weighted-average period of approximately 1.7 years. The value of share awards that vested during the years ended December 31, 2018, 2017 and 2016 was $24 million, $22 million and $16 million, respectively.