17. STOCK-BASED COMPENSATION PLANS

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As of June 30, 2021, we had approximately 7 million shares remaining under the stock-based compensation plans 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 annually over a three-year period.

The compensation cost from continuing operations under the stock-based compensation plans for our Company and Huntsman International were as follows (dollars in millions):

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The total income tax benefit recognized in the condensed consolidated statements of operations for us and Huntsman International for stock-based compensation arrangements was $1 million each for the six months ended June 30, 2021 and 2020.

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Stock Options

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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 average of the assumptions utilized for stock options granted during the periods.

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During each of the three months ended  June 30, 2021 and 2020, no stock options were granted.

A summary of stock option activity under the stock-based compensation plans as of June 30, 2021 and changes during the six months then ended is presented below:

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The weighted-average grant-date fair value of stock options granted during the six months ended June 30, 2021 was $11.48 per option. As of June 30, 2021, there was $8 million of total unrecognized compensation cost related to nonvested stock option arrangements granted under the stock-based compensation plans. That cost is expected to be recognized over a weighted-average period of approximately 1.9 years.

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The total intrinsic value of stock options exercised during the six months ended June 30, 2021 and 2020 was approximately $8 million and $2 million, respectively. Cash received from stock options exercised during each of the six months ended June 30, 2021 and 2020 was approximately $6 million and $1 million, respectively. The cash tax benefit from stock options exercised during each of the six months ended June 30, 2021 and 2020 was approximately $2 million and $1 million, respectively.

Nonvested Shares

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Nonvested shares granted under the stock-based compensation plans 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.

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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 six months ended June 30, 2021 and 2020, the weighted-average expected volatility rate was 44.8% and 34.0%, respectively, and the weighted average risk-free interest rate was 0.2% and 1.4%, respectively. For the performance share unit awards granted in the six months ended June 30, 2021 and 2020, 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.

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A summary of the status of our nonvested shares as of June 30, 2021 and changes during the six months then ended is presented below:

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As of June 30, 2021, there was $40 million of total unrecognized compensation cost related to nonvested share compensation arrangements granted under the stock-based compensation plans. That cost is expected to be recognized over a weighted-average period of approximately 2.1 years. The value of share awards that vested during the six months ended June 30, 2021 and 2020 was $18 million and $24 million, respectively.

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