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Description of Business and Significant Accounting Policies (Details)
$ / shares in Units, client in Thousands
 12 Months Ended
Mar. 21, 2025
Sep. 30, 2025
USD ($)
country
client
$ / shares
shares
Sep. 30, 2024
USD ($)
$ / shares
shares
Sep. 30, 2023
USD ($)
Significant Accounting Policies [Line Items]        
Number of countries in which entity operates (more than) | country   180    
Number of commercial, institutional and global payment clients (more than) | client   80    
Number of self-directed/retail clients (more than) | client   400    
Net liabilities denominated in argentine pesos   $ 900,000 $ 2,400,000  
Cash denominated in argentine pesos   900,000 3,000,000  
Net nonmonetary denominated in argentine pesos   3,600,000 2,700,000  
Cash held at banks and money market funds - segregated   4,321,100,000 2,789,400,000  
Securities segregated excluding warehouse receipts   804,500,000 0.0  
Commodities warehouse receipts   145,400,000 51,800,000  
Cash and cash equivalents - deposits and receivables   5,114,500,000 2,614,200,000  
US government securities and other securities - deposits and receivables   6,335,200,000 2,951,500,000  
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      
Treasury stock, shares (in shares) | shares   2,780,923 5,866,477  
Treasury stock, value   $ (32,800,000) $ (69,300,000)  
Treasury stock reissued (in shares) | shares   3,085,554    
Sale of stock, par value (in dollar per share) | $ / shares   $ 11.82    
Acquisition consideration shares reissued from treasury   $ 300,100,000    
Acquired finite-lived intangible asset, weighted average useful life   1 year    
Common stock, par value (in dollar per share) | $ / shares   $ 0.01 $ 0.01  
RJO        
Significant Accounting Policies [Line Items]        
Sale of stock, par value (in dollar per share) | $ / shares   $ 97.24    
Acquisition consideration shares reissued from treasury   $ 300,100,000    
Minimum        
Significant Accounting Policies [Line Items]        
Property plant and equipment, useful life   3 years    
Identifiable intangible assets amortization period   5 years    
Maximum        
Significant Accounting Policies [Line Items]        
Property plant and equipment, useful life   10 years    
Identifiable intangible assets amortization period   20 years    
Capitalized software development        
Significant Accounting Policies [Line Items]        
Property plant and equipment, useful life   3 years    
Argentina        
Significant Accounting Policies [Line Items]        
Translation gains   $ 2,800,000 $ 3,100,000 $ 6,600,000
Argentina | Revenue Benchmark | Geographic Concentration Risk        
Significant Accounting Policies [Line Items]        
Percentage of operating revenues (as a percent)   1.00%    
Self-Directed/Retail        
Significant Accounting Policies [Line Items]        
Number of countries in which entity operates (more than) | country   180