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Description of Business and Significant Accounting Policies (Details)
$ / shares in Units, client in Thousands
 12 Months Ended
Nov. 07, 2023
Sep. 30, 2024
USD ($)
client
country
$ / shares
shares
Sep. 30, 2023
USD ($)
$ / shares
shares
Sep. 30, 2022
USD ($)
Number of countries in which entity operates (more than) | country   180    
Number of commercial, institutional and global payment clients (more than) | client   54    
Number of self-directed/retail clients (more than) | client   400    
Net liabilities denominated in argentine pesos   $ 2,400,000 $ 200,000  
Cash denominated in argentine pesos (less than)   3,000,000 800,000  
Net nonmonetary denominated in argentine pesos   2,700,000 700,000  
Cash held at banks and money market funds - segregated   2,789,400,000 2,420,500,000  
Commodities warehouse receipts   51,800,000 5,800,000  
Cash and cash equivalents - deposits and receivables   2,614,200,000 2,512,900,000  
US government securities and other securities - deposits and receivables   $ 2,951,500,000 4,041,600,000  
Acquired finite-lived intangible asset, weighted average useful life   1 year    
Goodwill impairment charges   $ 0 0 $ 0
Intangible assets impairment charges   $ 0 $ 0 0
Preferred stock, authorized (in shares) | shares   1,000,000 1,000,000  
Preferred stock, par value (in dollar per share) | $ / shares   $ 0.01 $ 0.01  
Preferred stock, outstanding (in shares) | shares   0 0  
Stock split, conversion ratio 1.5      
Common stock, par value (in dollar per share) | $ / shares   $ 0.01 $ 0.01  
Minimum        
Property plant and equipment, useful life   3 years    
Identifiable intangible assets amortization period   5 years    
Maximum        
Property plant and equipment, useful life   10 years    
Identifiable intangible assets amortization period   20 years    
Capitalized software development        
Property plant and equipment, useful life   3 years    
Argentina        
Translation gains   $ 3,100,000 $ 6,600,000 $ 2,100,000
Argentina | Revenue Benchmark | Geographic Concentration Risk        
Percentage of operating revenues (as a percent)   1.00%    
Self-Directed/Retail        
Number of countries in which entity operates (more than) | country   180