<PAGE>   1
                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-K

[X]     ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE 
        SECURITIES EXCHANGE ACT OF 1934

                 FOR THE FISCAL YEAR ENDED:  DECEMBER 31, 1998
                                       OR

[ ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
        SECURITIES ACT OF 1934

            FOR THE TRANSITION PERIOD FROM __________ TO _________.

                     COMMISSION FILE NUMBER:  333-49015-01

 BEAR STEARNS ASSET BACKED SECURITIES, INC. (AS DEPOSITOR UNDER THE POOLING AND
   SERVICING AGREEMENT, DATED JUNE 1, 1998, PROVIDING FOR THE ISSUANCE OF THE
 AMERICAN RESIDENTIAL HOME EQUITY LOAN TRUST ASSET-BACKED CERTIFICATES, SERIES
                                    1998-1)

                   BEAR STEARNS ASSET BACKED SECURITIES, INC.
             (Exact Name of registrant as specified in its charter)

            DELAWARE                                    13-3836437
(State or other jurisdiction of             (I.R.S. employer identification no.)
incorporation or organization)

                 245 PARK AVENUE                          10167
                  NEW YORK, NY                          (Zip code)
    (Address of principal executive offices)

                                 (212) 272-4095
              (Registrant's telephone number, including area code)

<TABLE>
<S>                                                                   <C>              
Securities registered pursuant to Section 12(b) of the Act:           Securities registered pursuant to Section 12(g) of the Act:

                                NONE                                                                NONE
                          (Title of class)                                                    (Title of class)
</TABLE>

Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the Registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes [X]  No [ ]

Indicate by check mark if disclosure of delinquent filers pursuant to Item 405
of Regulation S-K is not contained herein, and will not be contained, to the
best of Registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. [X]

State the aggregate market value of the voting stock held by non-affiliates of
Registrant. The aggregate market value shall be computed by reference to the
price at which the stock was sold, or the average bid and asked prices of such
stock, as of specified date within 60 days prior to the date of filing:

                                 NOT APPLICABLE

                      Documents incorporated by reference:

                                 NOT APPLICABLE


<PAGE>   2
                   BEAR STEARNS ASSET-BACKED SECURIITIES, INC.
                           CERTIFICATES, SERIES 1998-1

                                      INDEX

<TABLE>
<CAPTION>
                                                                                                                         Page
                                                                                                                         ----
<S>                                                                                                                      <C>

PART I            ........................................................................................................ 3
                  ITEM 1  - BUSINESS...................................................................................... 3
                  ITEM 2  - PROPERTIES.................................................................................... 3
                  ITEM 3  - LEGAL PROCEEDINGS............................................................................. 3
                  ITEM 4  - SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS........................................... 3

PART II           ........................................................................................................ 3
                  ITEM 5  - MARKET FOR REGISTRANT'S COMMON STOCK AND RELATED STOCKHOLDER MATTERS.......................... 3
                  ITEM 6  - SELECTED FINANCIAL DATA....................................................................... 3
                  ITEM 7  - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS......... 3
                  ITEM 8  - FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA................................................... 3
                  ITEM 9  - CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND FINANCIAL DISCLOSURE.......... 3


PART III          ........................................................................................................ 4
                  ITEM 10 - DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT............................................ 4
                  ITEM 11 - EXECUTIVE COMPENSATION........................................................................ 4
                  ITEM 12 - SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT................................ 4
                  ITEM 13 - CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS................................................ 6

PART IV           ........................................................................................................ 6
                  ITEM 14 - EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K............................... 6

SIGNATURES        ........................................................................................................ 7
INDEX TO EXHIBITS .........................................................................................................8
</TABLE>


<PAGE>   3
                                     PART I

ITEM 1     -   BUSINESS

               Not Applicable.

ITEM 2     -   PROPERTIES

               Bear Stearns Asset-Backed Securities, Inc. (the "Depositor") will
furnish information regarding the Mortgaged Properties by reference to the
Annual Compliance Certificates to be filed herein under Item 14.

ITEM 3     -   LEGAL PROCEEDINGS

               The Depositor is not aware of any material pending legal
proceedings involving either the Asset-Backed Certificates, Series 1998-1 (the
"Trust); the Trustee; the Depositor; or the Servicer which relates to the Trust.

ITEM 4     -   SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

               No matter has been submitted to a vote of the holders of
beneficial interests in the Trust through the solicitation of proxies or
otherwise.

                                     PART II

ITEM 5     -   MARKET FOR REGISTRANT'S COMMON STOCK AND RELATED STOCKHOLDER
               MATTERS

               To the best knowledge of the Depositor, there is no established
public trading market for the Certificates.

               All of the Class A Certificates, Class M Certificates, Class B
Certificates, Class X Certificates and Class R Certificates issued by the Trust
are held by the Depository Trust Company ("DTC") which in turn maintains records
of holders of beneficial interests in such Certificates. Based on information
obtained by the Trust from DTC, as of December 31, 1998, there were six holders
of Class A-1 Certificates, and one holder of each of the Class M-1 Certificates,
Class M-2 Certificates, Class B Certificates, Class X Certificates and Class R
Certificates.

ITEM 6     -   SELECTED FINANCIAL DATA

               Not Applicable.

ITEM 7     -   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
               RESULTS OF OPERATIONS

               Not Applicable.

ITEM 8     -   FINANCIAL STATEMENTS AND SUPPLEMENTARY INFORMATION

               Not Applicable.

ITEM 9     -   CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
               FINANCIAL DISCLOSURE

               There were no changes of accountants or disagreements on
accounting or financial disclosures between the Depositor and its accountants.


<PAGE>   4
                                    PART III

ITEM 10    -   DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT

               Not Applicable.

ITEM 11    -   EXECUTIVE COMPENSATION

               Not Applicable.

ITEM 12    -   SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

               The following table sets forth (i) the name and address of each
entity owning more than 5% of the outstanding principal amount of each Class of
Certificates of the Trust; (ii) the principal amount of the Class of
Certificates owned by each and (iii) the percent that the principal amount of
the Class of Certificates owned by such entity represents of the outstanding
principal amount of such Class of Certificates. The information set forth in the
table for the Certificates is based upon information obtained by the Trust from
DTC and represents ownership of beneficial interest in the Certificates held by
DTC. The Depositor is not aware of any Schedules 13D or 13G filed with the
Securities and Exchange Commission in respect of the Certificates.

                                    Class A-1

<TABLE>
             NAME AND ADDRESS                     PRINCIPAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
The Bank of New York                                $18,000,000           21.47%
925 Patterson Plank Road
Secaucus, NJ  07094

Bear Stearns Securities Corporation                 $16,500,000           19.68%
One MetroTech Center North
4th Floor
Brooklyn, NY  11201-3862
                                                    $ 6,600,000            7.87%
Fiduciary Trust Company International
Two World Trade Center, 96th Floor
New York, NY  10048-0772

Bankers Trust Company                               $20,522,000           24.48%
C/O BT Services Tennessee Inc.
648 Grassmere Park Drive
Nashville, TN  37211

Boston Safe Deposit and Trust Company               $ 6,800,000            8.11%
C/C Mellon Bank N.A.
Three Mellon Bank Center, Room 153-3015
Pittsburgh, PA  15259

State Street Bank and Trust Company                 $15,400,000           18.37%
Global Corp Action Dept JAB5W
P.P. Box 1631
Boston, MA  02105-1631
</TABLE>

<PAGE>   5
                                    Class M-1

<TABLE>
             NAME AND ADDRESS                      NOTIONAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
Bear Stearns Securities Corporation                  $6,715,000           100%
One MetroTech Center North
4th Floor
Brooklyn, NY  11201-3862
</TABLE>


                                    Class M-2

<TABLE>
             NAME AND ADDRESS                      NOTIONAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
U.S. Bank National Association                       $4,228,000           100%
MPFP 1603 Proxy Unit
601 Second Avenue South
Minneapolis, MN  55402
</TABLE>


                                     Class B

<TABLE>
             NAME AND ADDRESS                      NOTIONAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
Bear Stearns Securities Corporation                  $3,376,000           100%
One Metrotech Center North
4th Floor
Brooklyn, NY  11201-3862
</TABLE>


                                     Class X

<TABLE>
             NAME AND ADDRESS                      NOTIONAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
Bear Stearns Securities Corporation                                       100%
One Metrotech Center North
4th Floor
Brooklyn, NY  11201-3862
</TABLE>


                                    Class R-1

<TABLE>
             NAME AND ADDRESS                     PRINCIPAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
Bear Stearns Securities Corporation                  0.01                 100%
One Metrotech Center North
4th Floor
Brooklyn, NY  11201-3862
</TABLE>


                                    Class R-2

<TABLE>
             NAME AND ADDRESS                     PRINCIPAL AMOUNT      % OF CLASS
<S>                                               <C>                   <C>   
Bear Stearns Securities Corporation                  1,000                100%
One Metrotech Center North
4th Floor
Brooklyn, NY  11201-3862
</TABLE>


<PAGE>   6
ITEM 13    -   CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

               None.

                                     PART IV

ITEM 14    -   EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K

               (a)     The following documents are filed as part of this
                       report:

                       1.      Financial Statements:

                               Not applicable.

                       2.      Financial Statement Schedules:

                               Not applicable.

                       3.      Exhibits:

                               Exhibit 
                                 No.               Description
                               -------             -----------

                                99.1*    Statement of Compliance of the Master
                                         Servicer.
                                       
                                99.2*    Annual Report of Independent Accountant
                                         with respect to the Master Servicer's
                                         overall servicing operations.
                                       
--------------                        
*The document is not due to be delivered until June 30, 1999. Such document will
be filed with the Securities and Exchange Commission by amendment upon receipt
by the Registrant.


<PAGE>   7
                                   SIGNATURES


           Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Depositor has duly caused this Report to be signed on
its behalf by the undersigned, thereunto duly authorized.


                               By:  AMERICAN RESIDENTIAL EAGLE INC.,
                                    As Depositor


                                    By: /s/ Mark A. Conger   
                                        --------------------------------------
                                    Name:   Mark A. Conger
                                    Title:  Executive Vice President, Chief
                                            Financial Officer

Date:      May 5, 1999.

           Pursuant to the requirements of the Securities Exchange Act of 1934,
this Report has been signed below by the following persons on behalf of the
Depositor and in the capacities and on the dates indicated:


<TABLE>
<CAPTION>
              Signature                                     Position                                        Date
              ---------                                     --------                                        ----
<S>                                           <C>                                                        <C> 
/s/ John R. Robbins                           Chief Executive Officer and                                May 5, 1999
--------------------------------------        Chairman of the Board of Directors
John R. Robbins                               (Principal Executive Officer)     
                                              

/s/ Jay M. Fuller                             President, Chief Operating Officer                         May 5, 1999
--------------------------------------        and Director
Jay M. Fuller                                 


/s/ Mark A. Conger                            Executive Vice President, Chief                            May 5, 1999
--------------------------------------        Financial Officer and Director
Mark A. Conger                                (Principal Financial and Accounting Officer)
                                              
</TABLE>


<PAGE>   8
                                INDEX TO EXHIBITS
                                   Item 14(C)

Exhibit No.  Description
-----------  -----------

99.1*        Statement of Compliance of the Master Servicer.

99.2*        Annual Report of Independent Accountant with respect to the Master
             Servicer's overall servicing operations.

--------------
*The document is not due to be delivered until June 30, 1999. Such document will
be filed with the Securities and Exchange Commission by amendment upon receipt
by the Registrant.