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Derivative Financial Instruments - Remaining Contract Maturity of Fair Value of OTC Derivative Assets and Liabilities (Details)
$ in Thousands
Aug. 31, 2025
USD ($)
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months $ 584,885
1 – 5 Years 304,241
Greater Than 5 Years 28,366
Cross-Maturity Netting (33,620)
Total OTC derivative assets, net of cross-maturity netting 883,872
Cross-product counterparty netting (35,717)
Total OTC derivative assets included in Financial instruments owned 848,155
0 – 12 Months 399,025
1 – 5 Years 510,190
Greater Than 5 Years 454,117
Cross-Maturity Netting (33,620)
Total OTC derivative liabilities, net of cross-maturity netting 1,329,712
Cross-product counterparty netting (35,717)
Total OTC derivative liabilities included in Financial instruments sold, not yet purchased 1,293,995
Exchange traded derivative assets, with fair value 1,160,000
Exchange traded derivative liabilities, with fair value 591,400
Cash collateral received 273,600
Cash collateral pledged 632,100
Commodity swaps, options and forwards  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 4,308
1 – 5 Years 0
Greater Than 5 Years 0
Cross-Maturity Netting 0
Total OTC derivative assets, net of cross-maturity netting 4,308
0 – 12 Months 2,829
1 – 5 Years 0
Greater Than 5 Years 0
Cross-Maturity Netting 0
Total OTC derivative liabilities, net of cross-maturity netting 2,829
Equity options and forwards  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 297,427
1 – 5 Years 7,350
Greater Than 5 Years 0
Cross-Maturity Netting (220)
Total OTC derivative assets, net of cross-maturity netting 304,557
0 – 12 Months 104,168
1 – 5 Years 323,381
Greater Than 5 Years 0
Cross-Maturity Netting (220)
Total OTC derivative liabilities, net of cross-maturity netting 427,329
Credit default swaps  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 0
1 – 5 Years 24,840
Greater Than 5 Years 0
Cross-Maturity Netting 0
Total OTC derivative assets, net of cross-maturity netting 24,840
0 – 12 Months 251
1 – 5 Years 9,583
Greater Than 5 Years 0
Cross-Maturity Netting 0
Total OTC derivative liabilities, net of cross-maturity netting 9,834
Total return swaps  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 137,965
1 – 5 Years 113,782
Greater Than 5 Years 0
Cross-Maturity Netting (15,878)
Total OTC derivative assets, net of cross-maturity netting 235,869
0 – 12 Months 161,468
1 – 5 Years 90,507
Greater Than 5 Years 37
Cross-Maturity Netting (15,878)
Total OTC derivative liabilities, net of cross-maturity netting 236,134
Foreign currency forwards, swaps and options  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 51,979
1 – 5 Years 863
Greater Than 5 Years 0
Cross-Maturity Netting (555)
Total OTC derivative assets, net of cross-maturity netting 52,287
0 – 12 Months 90,526
1 – 5 Years 420
Greater Than 5 Years 0
Cross-Maturity Netting (555)
Total OTC derivative liabilities, net of cross-maturity netting 90,391
Fixed income forwards  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 39,641
1 – 5 Years 0
Greater Than 5 Years 0
Cross-Maturity Netting 0
Total OTC derivative assets, net of cross-maturity netting 39,641
0 – 12 Months 5,839
1 – 5 Years 0
Greater Than 5 Years 0
Cross-Maturity Netting 0
Total OTC derivative liabilities, net of cross-maturity netting 5,839
Interest rate swaps, options and forwards  
Remaining Contract Maturity Of Fair Value Of Over Counter Derivative Assets And Liabilities [Line Items]  
0 – 12  Months 53,565
1 – 5 Years 157,406
Greater Than 5 Years 28,366
Cross-Maturity Netting (16,967)
Total OTC derivative assets, net of cross-maturity netting 222,370
0 – 12 Months 33,944
1 – 5 Years 86,299
Greater Than 5 Years 454,080
Cross-Maturity Netting (16,967)
Total OTC derivative liabilities, net of cross-maturity netting $ 557,356