<PAGE>   1
                                                                    EXHIBIT 10.2

                             CUSTODIAN AGREEMENT

         THIS CUSTODIAN AGREEMENT is made and entered into as of this ____ day
of _________________, 199__, between U.S.  Automobile Acceptance SNP-IV, Inc.,
a Texas corporation (the "Debtor"), Sterling Trust Company, as Trustee (the
"Secured Party") and U.S. Automobile Acceptance Corporation, a Texas
corporation (the "Custodian").

                              R E C I T A L S:

   
         A.      The Debtor has duly authorized the offer and sale of Callable
Asset-Backed Promissory Notes (the "Notes") in the aggregate principal sum of
up to $40,000,000, which Notes are backed by certain Collateral as set forth in
a Security Agreement between the Debtor and Secured Party.
    

         B.      In order to perfect its security interest in the Collateral as
granted under the Security Agreement, Secured Party has requested and Debtor
has agreed to deposit the Collateral with the Custodian subject to the terms
and conditions of this Agreement.

         1 .     The above recitals are true and correct and are incorporated
herein by reference.  All capitalized terms shall have the same meaning as in
the Security Agreement between Debtor and Secured Party of even date herewith.

         2.      Debtor or its Agent will deposit with Custodian the
Collateral.  The Custodian will have possession, custody and control of the
Collateral on behalf of the Secured Party and shall maintain the Collateral in
its possession.  The Custodian will have no responsibility for Collateral it
does not receive.

         3.      The Custodian will release to the Debtor each Contract and
related documents including the Vehicle Title constituting the Collateral upon
receipt of an affidavit signed and sworn to by a duly authorized officer of
Debtor that (a) Debtor has received payment in full from the obligor under the
Contract, (b) Debtor needs the contract and related documents to effect a
contract exchange or settlement under the terms of a recourse agreement, (c)
Debtor needs the Vehicle Title to repossess a Vehicle after default on a
Contract, or (d) any administrative event for which release for mailing to the
State is required under statute, rule, regulation or practice such as change in
name of Vehicle owner due to marriage or divorce, change of address Vehicle
owner, or notation of a subordinate lien on the Title.  Upon a release of a
Vehicle Title pursuant to 3(b) and (d) above, the Debtor or its Agent shall
promptly return the Vehicle Title or new exchanged title to the Custodian upon
receipt of the title after the changes have been made by the appropriate state
agency.  Upon an Event of Default on the Notes or in the Security Agreement,
Custodian shall deliver to the Trustee as representative of Secured Party all
Collateral promptly upon request of the Secured Party.

         4.      The Custodian undertakes to perform only such duties as are
expressly set forth herein, and no implied duties or obligations shall be read
into this Agreement against the Custodian.

         5.      The Custodian may without investigation act in reliance upon
any writing or instrument or signature which it, in good faith, believes to be
genuine, may assume without investigation the validity and accuracy of any
statement or assertion contained in such a writing or instrument, and may
assume without investigation that any person purporting to give any writing,
notice, advice or instructions in connection with the provisions hereof has
been duly authorized to do so.  The Custodian shall not be liable in any manner
for the sufficiency or correctness as to form, manner and execution, or
validity of any instrument deposited into this escrow, nor as to the identity,
authority or right of any person executing the same; and its duties hereunder
shall be limited to the safekeeping of such agreements, monies, instruments or
other documents received by it as such escrow holder, and for the disposition
of the same in accordance with the written instrument accepted by it in the
escrow or written instructions received by it.

         6.      The Debtor hereby agrees to indemnify the Custodian and hold
it harmless from any and all claims, liabilities, losses, actions, suits or
proceedings at law or in equity, or any other expenses, fees or charges of any
character or nature, which it may incur or with which it may be threatened by
reason of its acting as Custodian, against any and all expenses, including
attorneys' fees and the cost of defending any action, suit or proceeding or
resisting any claim.  The Custodian shall be vested with a lien on all property
deposited hereunder for indemnification, subject to the lien of the Trustee,
for attorneys' fees or charges of any character or nature, which may be
incurred by said Custodian by reason of disputes arising between the makers of
this escrow as to the correct interpretation of this Agreement and instructions
given to the Custodian hereunder, or otherwise, with the right of said
Custodian, regardless





                                      1
<PAGE>   2
of the instructions aforesaid to hold the said property until and unless said
additional expenses, fees and charges shall be fully paid.

         7.      If the parties be in disagreement about the interpretation of
this Custodian Agreement or about the rights and obligations or the propriety
or any action contemplated by the Custodian hereunder, the Custodian may, in
its sole discretion, file an action in interpleader to resolve the said
disagreement.  The Custodian shall be indemnified for all costs, including
reasonable attorneys' fees, in connection with the aforesaid interpleader
action, and shall be fully protected in suspending all or a part of its
activities under this Agreement until a final judgment in the interpleader
action is received.

         8.      The Custodian may consult with counsel of its own choice and
shall have full and complete authorization and protection for any action taken
or suffered by it hereunder in good faith and in accordance with the opinion of
such counsel.  The Custodian shall otherwise not be liable for any mistakes of
fact or error of judgment or for any acts or omissions of any kind unless
caused by its willful misconduct or gross negligence.

         9.      The Custodian may resign upon thirty days' written notice to
the parties in this Agreement.  If a successor Custodian is not appointed
within a thirty-day period, the Custodian may petition a court of competent
jurisdiction and name a successor.

         10.     The Debtor shall pay the Custodian such fees and compensation,
if any, as shall be mutually agreed.

         11.     The warranties, representations, covenants and agreements set
forth herein shall be continuous and shall survive the termination of this
Agreement or any part hereof.

         12.     This Agreement contains the entire understanding between the
parties hereto with respect to the transactions contemplated hereby, and this
Agreement supersedes in all respects all written or oral understandings and
agreements heretofore existing between the parties hereto.

         13.     This Agreement may not be modified or amended except by an
instrument in writing duly executed by the parties hereto.  No waiver of
compliance with any provision or condition hereof and no consent provided for
herein shall be effective unless evidenced by an instrument in writing duly
executed by the party hereto sought to be charged with such waiver or consent.

         14.     Notices and requests required or permitted hereunder shall be
deemed to be delivered hereunder if mailed with postage prepaid or delivered,
in writing.

         15.     This Agreement may be executed in one or more counterparts,
and all such counterparts shall constitute one and the same instrument

         16.     Captions used herein are for convenience only and are not a
part of this Agreement and shall not be used in construing it.

         17.     The parties to this Agreement acknowledge that the performance
of their respective obligations hereunder is essential to the consummation of
the transactions contemplated by this Agreement.  Each of them further
acknowledges that no party will have an adequate remedy at law if any other
party will have an adequate remedy at law if any other party fails to perform
its or their obligations hereunder.  In such event, each party shall have the
right, in addition to any other rights or remedies it may have, to compel
specific performance of this Agreement.

         18.     The Debtor shall reimburse the Custodian for any expenses in
connection with this Agreement and the transactions contemplated hereby,
including the fees and expenses of its counsel, certified public accountants
and other experts.

         19.     This Agreement shall not be assignable by any of the parties
to this Agreement without the prior written consent of all other parties to
this Agreement.

         20.     The parties to this Agreement agreed that jurisdiction and
venue shall properly lie  in Dallas County, Texas, with respect to any legal
proceedings arising from this Agreement.  Such jurisdiction and venue is merely





                                      2
<PAGE>   3
permissive; and jurisdiction and venue also shall continue to lie in any court
where jurisdiction and venue are found to be proper.  The parties further agree
that the mailing of any process shall constitute valid and lawful process
against them.

         21.     This Agreement has been negotiated and prepared in the State
of Texas, and the validity, construction and enforcement of, and the remedies
under, this Agreement shall be governed in accordance with the laws of the
State of Texas (except that if any choice of law provision under Texas law
would result in the application of the law of a state or jurisdiction other
than the State of Texas, such provision shall not apply).

         22.     The invalidity or unenforceability of any particular provision
hereof shall not affect the remaining provisions of this Agreement, and this
Agreement shall be construed in all respects as if such invalid or
unenforceable provision were omitted.

         23.     The rights and obligations of the parties hereunder shall
inure to the benefit of, and be binding and enforceable upon the respective
successors, assigns and transferees of either party.

         24.     This Custodian Agreement shall terminate and the Custodian
discharged of all responsibility hereunder at such time as the Custodian shall
receive a written affidavit signed and sworn to by a duly authorized officer of
Debtor that the Notes have been repaid in full or the Custodian has delivered
all Collateral to the Trustee as provided in paragraph 3.

         25.     Upon the occurrence of an Event of Default under the Notes or
the Security Documents, Custodian shall deliver to the Trustee all Collateral
in Custodian's possession.

         IN WITNESS WHEREOF, the parties hereto have executed this Custodian
Agreement on the day and year first above written.
                                    DEBTOR:

                                    U.S. AUTOMOBILE ACCEPTANCE SNP-IV, INC., a
                                    Texas Corporation

                                    By:
                                           -------------------------------------
                                    Its:
                                           -------------------------------------

                                    SECURED PARTY:

                                    STERLING TRUST COMPANY

                                    By:    
                                           -------------------------------------
                                    Its:
                                           -------------------------------------

                                    CUSTODIAN:

                                    U.S. AUTOMOBILE ACCEPTANCE CORPORATION
                                    a Texas corporation

                                    By:
                                           -------------------------------------
                                    Its:
                                           -------------------------------------






                                      3