Derivative Financial Instruments - Remaining Contract Maturity of Fair Value of OTC Derivative Assets and Liabilities (Details) $ in Thousands	Aug. 31, 2022 USD ($)
OTC Derivative Assets [Abstract]
0 – 12 Months	$ 451,828
1 – 5 Years	569,116
Greater Than 5 Years	27,589
Cross-Maturity Netting	(164,446)
Total OTC derivative assets, net of cross-maturity netting	884,087
Cross product counterparty netting	(27,872)
Total OTC derivative assets included in Financial instruments owned	856,215
OTC Derivative Liabilities [Abstract]
0 – 12 Months	704,793
1 – 5 Years	942,747
Greater Than 5 Years	521,563
Cross-Maturity Netting	(164,446)
Total OTC derivative liabilities, net of cross-maturity netting	2,004,657
Cross product counterparty netting	(27,872)
Total OTC derivative liabilities included in Financial instruments sold, not yet purchased	1,976,785
Exchange traded derivative assets, with fair value	266,000
Cash collateral received	748,300
Exchange traded derivative liabilities, with fair value	51,800
Cash collateral pledged	579,600
Equity options and forwards
OTC Derivative Assets [Abstract]
0 – 12 Months	17,773
1 – 5 Years	5,488
Greater Than 5 Years	0
Cross-Maturity Netting	(4,600)
Total OTC derivative assets, net of cross-maturity netting	18,661
OTC Derivative Liabilities [Abstract]
0 – 12 Months	115,856
1 – 5 Years	290,887
Greater Than 5 Years	26,180
Cross-Maturity Netting	(4,600)
Total OTC derivative liabilities, net of cross-maturity netting	428,323
Credit default swaps
OTC Derivative Assets [Abstract]
0 – 12 Months	0
1 – 5 Years	3,371
Greater Than 5 Years	255
Cross-Maturity Netting	0
Total OTC derivative assets, net of cross-maturity netting	3,626
OTC Derivative Liabilities [Abstract]
0 – 12 Months	0
1 – 5 Years	620
Greater Than 5 Years	0
Cross-Maturity Netting	0
Total OTC derivative liabilities, net of cross-maturity netting	620
Total return swaps
OTC Derivative Assets [Abstract]
0 – 12 Months	101,046
1 – 5 Years	15,879
Greater Than 5 Years	194
Cross-Maturity Netting	(6,538)
Total OTC derivative assets, net of cross-maturity netting	110,581
OTC Derivative Liabilities [Abstract]
0 – 12 Months	373,151
1 – 5 Years	104,255
Greater Than 5 Years	3
Cross-Maturity Netting	(6,538)
Total OTC derivative liabilities, net of cross-maturity netting	470,871
Foreign currency forwards, swaps and options
OTC Derivative Assets [Abstract]
0 – 12 Months	202,065
1 – 5 Years	6,938
Greater Than 5 Years	170
Cross-Maturity Netting	(5,038)
Total OTC derivative assets, net of cross-maturity netting	204,135
OTC Derivative Liabilities [Abstract]
0 – 12 Months	107,227
1 – 5 Years	6,156
Greater Than 5 Years	47
Cross-Maturity Netting	(5,038)
Total OTC derivative liabilities, net of cross-maturity netting	108,392
Fixed income forwards
OTC Derivative Assets [Abstract]
0 – 12 Months	14,191
1 – 5 Years	0
Greater Than 5 Years	0
Cross-Maturity Netting	0
Total OTC derivative assets, net of cross-maturity netting	14,191
OTC Derivative Liabilities [Abstract]
0 – 12 Months	54
1 – 5 Years	0
Greater Than 5 Years	0
Cross-Maturity Netting	0
Total OTC derivative liabilities, net of cross-maturity netting	54
Interest rate swaps, options and forwards
OTC Derivative Assets [Abstract]
0 – 12 Months	116,753
1 – 5 Years	537,440
Greater Than 5 Years	26,970
Cross-Maturity Netting	(148,270)
Total OTC derivative assets, net of cross-maturity netting	532,893
OTC Derivative Liabilities [Abstract]
0 – 12 Months	108,505
1 – 5 Years	540,829
Greater Than 5 Years	495,333
Cross-Maturity Netting	(148,270)
Total OTC derivative liabilities, net of cross-maturity netting	$ 996,397