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Stock Options and Stock Appreciation Rights | 12 Months Ended
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Dec. 31, 2022
Stock Options | (15) Stock Options and Stock Appreciation Rights On April 5, 2012, the Board of Directors adopted the 2012 International Bancshares Corporation Stock Option Plan (the “2012 Plan”). There are 800,000 shares available for stock option grants under the 2012 Plan. Under the 2012 Plan, both qualified incentive stock options (“ISOs”) and non-qualified stock options (“NQSOs”) may be granted. Options granted may be exercisable for a period of up to 10 years from the date of grant, excluding ISOs granted to 10% shareholders, which may be exercisable for a period of up to only five years. On April 4, 2022, the 2012 Plan expired and was not renewed. The fair value of each option award granted under the plan is estimated on the date of grant using a Black-Scholes-Merton option valuation model that uses the assumptions noted in the following table. Expected volatility is based on the historical volatility of the price of our stock. We use historical data to estimate the expected dividend yield and employee termination rates within the valuation model. The expected term of options is derived from historical exercise behavior. The risk-free rate for periods within the contractual life of the option is based on the U.S. Treasury yield curve in effect at the time of grant. ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | 2022 |  | 2021 |
Expected Life (Years) |  | 7.00 | ​ | 7.00 | ​
Dividend yield |  | 3.08 | % | 3.18 | %
Interest rate |  | 1.94 | % | 1.02 | %
Volatility |  | 37.78 | % | 37.84 | %
​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​
​ A summary of option activity under the stock option plans for the twelve months ended December 31, 2022 is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | ​ | ​ |  | Weighted |  |  | ​ | ​
​ | ​ | ​ | ​ | Weighted | ​ | average | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | average | ​ | remaining | ​ | Aggregate | ​
​ | ​ | Number of | ​ | exercise | ​ | contractual | ​ | intrinsic | ​
​ | ​ | options | ​ | price | ​ | term (years) | ​ | value ($) | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | (in Thousands) | ​
Options outstanding at December 31, 2021 |  | 520,551 | ​ | $ | 28.28 | ​ | ​ | ​ | ​ | ​ | ​
Plus: Options granted |  | 31,150 | ​ |  | 38.92 | ​ | ​ | ​ | ​ | ​ | ​
Less: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Options exercised |  | 69,479 | ​ |  | 22.14 | ​ | ​ | ​ | ​ | ​ | ​
Options expired |  | — | ​ |  | — | ​ | ​ | ​ | ​ | ​ | ​
Options forfeited |  | 20,400 | ​ |  | 33.99 | ​ | ​ | ​ | ​ | ​ | ​
Options outstanding at December 31, 2022 |  | 461,822 | ​ |  | 29.67 |  | 4.07 | ​ | $ | 7,430 | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Options fully vested and exercisable at December 31, 2022 |  | 258,215 | ​ | $ | 25.26 |  | 2.26 | ​ | $ | 5,293 | ​
​ Stock-based compensation expense included in the consolidated statements of income for the years ended December 31, 2022, 2021 and 2020 was approximately $449,000, $506,000 and $743,000, respectively. As of December 31, 2022, there was approximately $762,000 of total unrecognized stock-based compensation cost related to non-vested options granted under our plans that will be recognized over a weighted average period of 1.7 years. Other information pertaining to option activity during the twelve months ended December 31, 2022, 2021 and 2020 is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Twelve Months Ended December 31, |
​ | ​ | 2022 | ​ | 2021 | ​ | 2020 |
Weighted average grant date fair value of stock options granted |  | $ | 11.24 |  | $ | 10.20 |  | $ | 2.46 | ​
Total fair value of stock options vested | ​ | $ | 514,000 | ​ | $ | 1,308,000 | ​ | $ | 1,218,000 | ​
Total intrinsic value of stock options exercised | ​ | $ | 1,670,000 | ​ | $ | 2,536,000 | ​ | $ | 356,000 | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​
​ ​ ​ ​ ​ On April 18, 2022, the Board of Directors adopted the 2022 International Bancshares Stock Appreciation Rights Plan (the “SAR Plan”). There are 750,000 shares of underlying common stock that may be used for stock appreciation right (“SAR”) grants under the plan, however, no actual shares will be granted. Upon exercise, the SAR will be settled in cash. SARs granted may be exercisable for a period of up to 10 years from the date of grant and may vest over an eight-year period. As of December 31, 2022, a total of 502,250 SARS had been issued under the SAR Plan. ​ A summary of activity under the SAR Plan for the twelve months ended December 31, 2022 is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | ​ | ​ |  | Weighted |  |  | ​
​ | ​ | ​ | ​ | Weighted | ​ | average | ​ | ​ | ​
​ | ​ | Number of | ​ | average | ​ | remaining | ​ | Aggregate
​ | ​ | stock appreciation | ​ | exercise | ​ | contractual | ​ | intrinsic
​ | ​ | rights | ​ | price | ​ | term (years) | ​ | value ($)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | (in Thousands)
Stock appreciation rights outstanding at December 31, 2021 |  | — | ​ | $ | — | ​ | ​ | ​ | ​ | ​
Plus: Stock appreciation rights granted |  | 502,250 | ​ | ​ | 39.95 | ​ | ​ | ​ | ​ | ​
Less: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Stock appreciation rights exercised |  | — | ​ | ​ | — | ​ | ​ | ​ | ​ | ​
Stock appreciation rights expired |  | — | ​ | ​ | — | ​ | ​ | ​ | ​ | ​
Stock appreciation rights forfeited |  | 13,000 | ​ | ​ | 39.33 | ​ | ​ | ​ | ​ | ​
Stock appreciation rights outstanding at December 31, 2022 |  | 489,250 | ​ |  | 39.35 |  | 9.50 | ​ | $ | 3,136
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Stock appreciation rights fully vested and exercisable at December 31, 2022 |  | — | ​ | $ | — |  | ​ | ​ | ​ | ​
​ The fair value of the liability for payments due to stock appreciation rights holders at December 31, 2022 is approximately $546,000, as calculated using a Black-Sholes Merton model, and is included in other liabilities on the consolidated statements of condition. The expense recorded in connection with all grants under the SAR Plan totaled $546,000 for the twelve months ended December 31, 2022. ​ ​

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