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Stock Options and Stock Appreciation Rights | 12 Months Ended
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Dec. 31, 2025
Stock Options and Stock Appreciation Rights |
Stock Options and Stock Appreciation Rights | (14) 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 were 800,000 shares of common stock available for stock option grants under the 2012 Plan, which were qualified incentive stock options (“ISOs”) or non-qualified stock options. 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 was 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 was based on the historical volatility of the price of our stock. We used historical data to estimate the expected dividend yield and employee termination rates within the valuation model. The expected term of options was derived from historical exercise 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. ​ A summary of option activity under the stock option plans for the twelve months ended December 31, 2025 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, 2024 |  | 212,155 | ​ | $ | 35.27 | ​ | ​ | ​ | ​ | ​ | ​
Plus: Options granted |  | — | ​ | ​ | — | ​ | ​ | ​ | ​ | ​ | ​
Less: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Options exercised |  | (42,121) | ​ | ​ | 34.81 | ​ | ​ | ​ | ​ | ​ | ​
Options expired |  | — | ​ | ​ | — | ​ | ​ | ​ | ​ | ​ | ​
Options forfeited |  | (5,150) | ​ | ​ | 34.03 | ​ | ​ | ​ | ​ | ​ | ​
Options outstanding at December 31, 2025 |  | 164,884 | ​ |  | 35.42 |  | 3.37 | ​ | $ | 5,115 | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Options fully vested and exercisable at December 31, 2025 |  | 122,733 | ​ | $ | 36.20 |  | 2.65 | ​ | $ | 3,711 | ​
​ Stock-based compensation expense included in the consolidated statements of income for the years ended December 31, 2025, 2024, and 2023 was approximately $104,000, $214,000, and $330,000, respectively. As of December 31, 2025, there was approximately $113,000 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 1.2 years. Other information pertaining to option activity during the twelve months ended December 31, 2025, 2024, and 2023 is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Twelve Months Ended December 31, |
​ | ​ | 2025 | ​ | 2024 | ​ | 2023 |
Weighted average grant date fair value of stock options granted | ​ ​ ​ | $ | — | ​ ​ ​ | $ | — | ​ ​ ​ | $ | — | ​
Total fair value of stock options vested | ​ | $ | 478,000 | ​ | $ | 616,286 | ​ | $ | 514,000 | ​
Total intrinsic value of stock options exercised | ​ | $ | 1,314,000 | ​ | $ | 4,640,000 | ​ | $ | 1,060,000 | ​
​ 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, 2025, a total of 426,743 SARS had been issued under the SAR Plan. ​ A summary of activity under the SAR Plan for the twelve months ended December 31, 2025 is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ ​ ​ | ​ | ​ ​ ​ | ​ | ​ | ​ ​ ​ | Weighted | ​ ​ ​ | ​ ​ ​ | ​
​ | ​ | ​ | ​ | Weighted | ​ | average | ​ | ​ | ​
​ | ​ | Number of | ​ | average | ​ | remaining | ​ | Aggregate
​ | ​ | stock appreciation | ​ | exercise | ​ | contractual | ​ | intrinsic
​ | ​ | rights | ​ | price | ​ | term (years) | ​ | value ($)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | (in Thousands)
SARs outstanding at December 31, 2024 |  | 456,702 | ​ | $ | 39.61 | ​ | ​ | ​ | ​ | ​
Plus: SARs granted |  | — | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Less: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
SARs exercised |  | (11,583) | ​ | ​ | 39.33 | ​ | ​ | ​ | ​ | ​
SARs expired |  | — | ​ | ​ | — | ​ | ​ | ​ | ​ | ​
SARs forfeited |  | (18,376) | ​ | ​ | 39.33 | ​ | ​ | ​ | ​ | ​
SARs outstanding at December 31, 2025 |  | 426,743 | ​ |  | 39.63 | ​ | 6.54 | ​ | $ | 11,443
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
SARs fully vested and exercisable at December 31, 2025 |  | 62,811 | ​ | $ | 39.35 |  | 6.50 | ​ | $ | 1,701
​ The fair value of the liability for payments due to stock appreciation rights holders at December 31, 2025 and December 31, 2024 is approximately $6,620,000 and $4,540,000, respectively, as calculated using a Black-Scholes-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 $2,131,000, $3,144,000, and $918,000, respectively, for the twelve months ended December 31, 2025, 2024, and 2023. As of December 31, 2025, there was approximately $6,810,000 in unrecognized liability related to non-vested SARs granted under the plan that will be recognized over a weighted average period of 6.5 years. ​ ​

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