PRICING SUPPLEMENT NO.  37                                        Rule 424(b)(3)
DATED: October 3, 2002                                        File No. 333-76894
(To Prospectus dated January 25, 2002,
and Prospectus Supplement dated January 25, 2002)

                                 $10,006,693,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount: $75,000,000    Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 10/8/2002   Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date: 10/8/2003         CUSIP#: 073928XT5

Option to Extend Maturity:       No  [x]
                                 Yes [ ] Final Maturity Date:

                                              Optional            Optional
                         Redemption           Repayment           Repayment
   Redeemable On          Price(s)             Date(s)            Price(s)
   -------------          --------             -------            --------

        N/A                  N/A                 N/A                 N/A

Applicable Only to Fixed Rate Notes:
------------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
---------------------------------------

Interest Rate Basis:                    Maximum Interest Rate: N/A

[ ] Commercial Paper Rate               Minimum Interest Rate: N/A

[ ] Federal Funds Effective Rate

[ ] Federal Funds Open Rate             Interest Reset Date(s): *

[ ] Treasury Rate                       Interest Reset Period: Monthly

[ ] LIBOR Reuters                       Interest Payment Date(s): **

[x] LIBOR Telerate

[ ] Prime Rate

[ ] CMT Rate

Initial Interest Rate: 1.81%            Interest Payment Period: Monthly

Index Maturity: One Month

Spread (plus or minus): +0.01%

* On the 8th of each month prior to Maturity.

** On the 8th of each month and at Maturity.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.