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Stock-Based Compensation
 3 Months Ended
Jan. 31, 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 
 January 31,
 20242023
 (in thousands)
Cost of products$20,680 $16,029 
Cost of maintenance and service9,176 7,155 
Research and development expense94,888 69,231 
Sales and marketing expense35,353 24,907 
General and administrative expense20,555 16,905 
Stock-based compensation expense before taxes180,652 134,227 
Income tax benefit(29,410)(21,570)
Stock-based compensation expense after taxes$151,242 $112,657 
During the three months ended January 31, 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 
 January 31,
 20242023
Expected life (in years)2.89 years0.90 years
Risk-free interest rate4.41 %4.63 %
Volatility34.03 %42.86 %
Grant date fair value$600.29 $408.55 
As of January 31, 2024, 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 2.7 years. As of January 31, 2024, we had $27.5 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,
 20242023
 (in thousands)
Intrinsic value of awards exercised$27,855 $54,776