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Stock-Based Compensation
 3 Months Ended
Jan. 31, 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 
 January 31,
 20252024
 (in thousands)
Cost of products$20,477 $16,261 
Cost of maintenance and service8,991 9,176 
Research and development expense102,696 91,137 
Sales and marketing expense34,950 30,573 
General and administrative expense19,349 18,358 
Stock-based compensation expense from continuing operations before taxes
186,463 165,505 
Stock-based compensation expense from discontinued operations before taxes
— 15,147 
Total stock-based compensation expense before taxes
186,463 180,652 
Income tax benefit(30,655)(29,410)
Stock-based compensation expense after taxes$155,808 $151,242 
During the three months ended January 31, 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 
 January 31,
 20252024
Expected life (in years)
2.79 years
2.89 years
Risk-free interest rate
4.39%
4.41%
Volatility
34.72%
34.03%
Grant date fair value
$464.17
$600.29
As of January 31, 2025, we had $1.6 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 2.4 years. As of January 31, 2025, we had $88.7 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 
 January 31,
 20252024
 (in thousands)
Intrinsic value of awards exercised$20,359 $27,855