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Stock-Based Compensation
 6 Months Ended
Apr. 30, 2025
Share-Based Payment Arrangement [Abstract]  
Stock-Based Compensation Stock-Based Compensation
The compensation cost recognized in the condensed consolidated statements of income for our stock compensation arrangements is as follows:
 Three Months Ended 
 April 30,		Six Months Ended 
 April 30,
 2025202420252024
 (in thousands)
Cost of products$23,050 $13,918 $43,527 $30,179 
Cost of maintenance and service9,502 9,273 18,493 18,449 
Research and development expense109,717 88,671 212,413 179,808 
Sales and marketing expense36,700 30,987 71,650 61,560 
General and administrative expense22,754 19,842 42,103 38,200 
Stock-based compensation expense from continuing operations before taxes
201,723 162,691 388,186 328,196 
Stock-based compensation expense from discontinued operations before taxes
— 15,144 — 30,291 
Total stock-based compensation expense before taxes
201,723 177,835 388,186 358,487 
Income tax benefit(32,659)(28,809)(62,847)(58,075)
Stock-based compensation expense after taxes$169,064 $149,026 $325,339 $300,412 
During the three and six months ended April 30, 2025 and 2024, we recognized stock-based compensation expense relating to restricted stock units (RSUs) granted to senior executives with certain market, performance and service conditions (market-based RSUs). The grant date fair value of the market-based RSUs and the assumptions used in the Monte Carlo simulation model to determine the grant date fair value during the periods are as follows:
 Three Months Ended 
 April 30,		Six Months Ended 
 April 30,
 2025202420252024
Expected life (in years)2.67 years— 
2.67 years - 2.79 years
2.89 years
Risk-free interest rate3.90 %— 
3.90% - 4.39%
4.41%
Volatility33.40 %— 
33.40% - 34.72%
34.03%
Grant date fair value$409.94— 
$409.94 - $464.17
$600.29
As of April 30, 2025, we had $1.5 billion of total unrecognized stock-based compensation expense relating to options, RSUs and restricted stock awards, which is expected to be recognized over a weighted-average period of 2.2 years. As of April 30, 2025, we had $154.8 million of unrecognized stock-based compensation expense relating to our Employee Stock Purchase Plan, which is expected to be recognized over a period of approximately 2.0 years.
The intrinsic values of equity awards exercised during the periods are as follows:
 Three Months Ended 
 April 30,		Six Months Ended 
 April 30,
 2025202420252024
 (in thousands)
Intrinsic value of awards exercised$34,479 $48,164 $54,837 $76,019