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Stock-Based Compensation
 6 Months Ended
Apr. 30, 2024
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,
 2024202320242023
 (in thousands)
Cost of products$13,918 $12,961 $30,179 $25,362 
Cost of maintenance and service9,273 7,531 18,449 14,686 
Research and development expense88,671 72,346 179,808 138,880 
Sales and marketing expense30,987 22,971 61,560 44,397 
General and administrative expense19,842 14,551 38,200 29,633 
Stock-based compensation expense from continuing operations before taxes
162,691 130,360 328,196 252,958 
Stock-based compensation expense from discontinued operations before taxes
15,144 12,898 30,291 24,527 
Total stock-based compensation expense before taxes
177,835 143,258 358,487 277,485 
Income tax benefit(28,809)(23,193)(58,075)(44,925)
Stock-based compensation expense after taxes$149,026 $120,065 $300,412 $232,560 
During the three and six months ended April 30, 2024 and 2023, 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 were as follows:
 Three Months Ended 
 April 30,		Six Months Ended 
 April 30,
 2024202320242023
Expected life (in years)— 2.70 years
2.89 years
0.90 years - 2.70 years
Risk-free interest rate— 4.36 %
4.41%
4.36% - 4.63%
Volatility— 35.84 %
34.03%
35.84% - 42.86%
Grant date fair value— $357.29 
$600.29
$357.29 - $408.55
As of April 30, 2024, we had $1.5 billion of total unrecognized stock-based compensation expense from continuing and discontinued operations relating to options, RSUs and restricted stock awards, which is expected to be recognized over a weighted-average period of 2.5 years. As of April 30, 2024, we had $85.8 million of unrecognized stock-based compensation expense from continuing and discontinued operations 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 from continuing and discontinued operations during the periods are as follows:
 Three Months Ended 
 April 30,		Six Months Ended 
 April 30,
 2024202320242023
 (in thousands)
Intrinsic value of awards exercised$48,164 $63,447 $76,019 $118,223