<PAGE>

                                                                    Exhibit 10.5


================================================================================


                           MBIA INSURANCE CORPORATION,
                                   as Insurer,



                         CAPITAL ONE AUTO FINANCE, INC.
                                       and

                        CAPITAL ONE AUTO RECEIVABLES, LLC
                                as Issuer Parties


                                       and



                     CREDIT SUISSE FIRST BOSTON CORPORATION,
                      as Representative of the Underwriters




                            INDEMNIFICATION AGREEMENT



                                 $1,200,000,000
                      Capital One Auto Finance Trust 2001-B
                Automobile Receivable-Backed Notes, Series 2001-B
                Class A-1 Notes, Class A-2 Notes, Class A-3 Notes
                               and Class A-4 Notes


                          Dated as of December 13, 2001



================================================================================

<PAGE>

                            INDEMNIFICATION AGREEMENT

     This AGREEMENT, dated as of December 13, 2001 is between MBIA INSURANCE
CORPORATION (the "Insurer"), as the Insurer under the Note Guaranty Insurance
Policy (the "Policy") issued in connection with the Offered Notes described
below, CAPITAL ONE AUTO FINANCE, INC. ("COAF"), CAPITAL ONE AUTO RECEIVABLES,
LLC ("COAR," and together with COAF, the "Issuer Parties") and CREDIT SUISSE
FIRST BOSTON CORPORATION ("CSFB"), as Representative of the Underwriters (the
"Representative") on behalf of the Underwriters (as defined below).

     Section 1. Definitions. As used in this Agreement, the following terms
shall have the respective meanings stated herein, unless the context clearly
requires otherwise, in both singular and plural form, as appropriate.
Capitalized terms used in this Agreement but not otherwise defined herein will
have the meanings ascribed to such terms in the Indenture (as described below).

     "Act" means the Securities Act of 1933, as amended, together with all
related rules and regulations.

     "Agreement" means this Indemnification Agreement by and between the Insurer
and the Representative of the Underwriters.

     "Indemnified Party" means any party entitled to any indemnification
pursuant to Section 5 below, as the context requires.

     "Indemnifying Party" means any party required to provide indemnification
pursuant to Section 5 below, as the context requires.

     "Indenture" means the Indenture dated as of December 20, 2001 by and
between the Wilmington Trust Company, as Owner Trustee, and JP Morgan Chase
Bank, as Indenture Trustee.

     "Insurance Agreement" means the Insurance Agreement, dated as of December
20, 2001 by and among the Insurer, the Owner Trustee, the Seller, the
Transferor, the Servicer, the Indenture Trustee and Owner Trustee.

     "Insurer Party" means the Insurer and its respective parents, subsidiaries
and affiliates and any shar'eholder, director, officer, employee, agent or any
"controlling person" (as such term is used in the Act) of any of the foregoing.

<PAGE>

     "Issuer Party" means each of COAF and COAR and its parent, subsidiaries,
and affiliates and any member, shareholder, director, officer, employee, agent
or any "controlling person" (as such term is used in the Act) of any of the
following.

     "Losses" means (i) any actual out-of-pocket loss paid by the party entitled
to indemnification or contribution hereunder and (ii) any actual out-of-pocket
costs and expenses paid by such party, including reasonable fees and expenses of
its counsel, to the extent not paid, satisfied or reimbursed from funds provided
by any other Person (provided that the foregoing shall not create or imply any
obligation to pursue recourse against any such other Person).

     "Offered Notes" means the Capital One Auto Finance Trust 2001-B Automobile
Receivable-Backed Notes, Series 2001-B, Class A-1, Class-A-2, Class-A-3 and
Class-A-4, issued in accordance with the provisions of the Indenture.

     "Person" means any individual, partnership, joint venture, corporation,
trust or unincorporated organization or any government or agency or political
subdivision thereof.

     "Prospectus Supplement" means the Preliminary Prospectus Supplement dated
December 11, 2001 and the Prospectus Supplement dated December 13, 2001 with
respect to the Offered Notes.

     "Servicer" means Capital One Auto Finance, Inc. as the Servicer of the
Receivables or any other Eligible Servicer acting as servicer pursuant to the
Servicing Agreement. Unless the context otherwise requires "Servicer" also
refers to any successor Servicer appointed under the Indenture or pursuant to
the Servicing Agreement.

     "Servicing Agreement" means the Servicing Agreement dated as of December
20, 2001 by and among the Owner Trustee, the Indenture Trustee and the Servicer.

     "Underwriter Party" means, with respect to the Underwriters, each such
Underwriter and its parent, subsidiaries and affiliates and any shareholder,
director, officer, employee, agent or "controlling person" (as such term is used
in the Act) of any of the foregoing.

     "Underwriting Agreement" means the Underwriting Agreement by and among
COAF, Capital One Auto Receivables, LLC and CSFB, as representative for the
Underwriters dated as of December 13, 2001.

     "Underwriters" and "Underwriter" means, in plural form, CSFB, Banc of
America Securities LLC, Deutsche Banc Alex. Brown and First Union Securities,
Inc. and in singular form, each of CSFB, Banc of America Securities LLC,
Deutsche Banc Alex. Brown and First Union Securities, Inc.

                                       2

<PAGE>

     Section 2. Representations and Warranties of the Insurer. The Insurer
represents and warrants to each Underwriter and the each Issuer Party as
follows:

          (a) Organization and Licensing. The Insurer is a duly incorporated and
existing New York stock insurance company licensed to do business in the State
of New York and is in good standing under the laws of such state.

          (b) Corporate Power. The Insurer has the corporate power and authority
to issue the Policy and execute and deliver this Agreement and to perform all of
its obligations hereunder and thereunder.

          (c) Authorization; Approvals. The issuance of the Policy and the
execution, delivery and performance of this Agreement have been duly authorized
by all necessary corporate proceedings. No further approvals or filings of any
kind, including, without limitation, any further approvals of or further filings
with any governmental agency or other governmental authority, or any approval of
the Insurer's board of directors or stockholders, are necessary for the Policy
and this Agreement to constitute the legal, valid and binding obligations of the
Insurer.

          (d) Enforceability. The Policy, when issued, and this Agreement will
each constitute a legal, valid and binding obligation of the Insurer,
enforceable in accordance with its terms, subject to applicable laws affecting
the enforceability of creditors' rights generally.

          (e) Financial Information. The consolidated financial statements of
the Insurer and its subsidiaries as of December 31, 2000 and December 31, 1999
and for each of the three years in the period ended December 31, 2000
incorporated by reference in the Prospectus Supplement (the "Insurer Audited
Financial Statements"), fairly present in all material respects the financial
condition of the Insurer as of such date and for the period covered by such
statements in accordance with generally accepted accounting principles
consistently applied. The consolidated financial statements of the Insurer and
its subsidiaries as of September 30, 2001 and for the nine month periods ended
September 30, 2001 and September 30, 2000 incorporated by reference in the
Prospectus Supplement (the "Insurer Unaudited Financial Statements"; the Insurer
Audited Financial Statements and the Insurer Unaudited Financial Statements are
referred to herein as the "Insurer Financial Statements") present fairly in all
material respects the financial condition of the Insurer as of such date and for
the period covered by such statements in accordance with generally accepted
accounting principles applied in a manner consistent with the accounting
principles used in preparing the Insurer Audited Financial Statements, and since
September 30, 2001, there has been no material change in such financial
condition of the Insurer which would materially and adversely affect its ability
to perform its obligations under the Policy.

          (f) Insurer Information. The information in the Prospectus Supplement
of the date hereof under the caption "THE Note Guaranty Insurance Policy AND THE
NOTE INSURER" (the "Insurer Information") is limited and does not purport to
provide the

                                       3

<PAGE>

scope of disclosure required to be included in a prospectus for a registrant
under the Securities Act of 1933, in connection with the public offer and sale
of securities of such registrant. Within such limited scope of disclosure, the
Insurer Information does not contain any untrue statement of a material fact or
omit to state a material fact necessary to make the statements therein, in light
of the circumstances under which they were made, not misleading.

          (g) No Litigation. There are no actions, suits, proceedings or
investigations pending or, to the best of the Insurer's knowledge, threatened
against it at law or in equity or before or by any court, governmental agency,
board or commission or any arbitrator which, if decided adversely, would
materially and adversely affect its condition (financial or otherwise) or
operations of it or would materially and adversely affect its ability to perform
its obligations under this Agreement or the Policy.

     Section 3. Representations and Warranties of the Underwriters. Each
Underwriter severally represents and warrants (only with respect to itself) to
the Insurer as follows:

          (a) Prospectus Supplement. It represents and warrants to and agrees
with the Insurer that the statements in the Prospectus Supplement made in
reliance upon and in conformity with written information relating to such
Underwriter furnished to Capital One Auto Finance, Inc. specifically for use in
the preparation of the Prospectus Supplement, and acknowledged in writing set
forth in the second paragraph (regarding concessions and discounts) and the
first sentence of the eighth paragraph (regarding marketmaking) under the
caption "Underwriting" in the Prospectus Supplement (referred to herein as the
"Underwriter Information"), are true and correct in all material respects.

          (b) Corporate Power. It has the corporate power and authority to
execute and deliver this Agreement and the Underwriting Agreement and to perform
all of its obligations hereunder and thereunder in all material respects.

          (c) Authorization; Approvals. The execution, delivery and performance
of this Agreement and the Underwriting Agreement by such Underwriter have been
duly authorized by all necessary corporate proceedings. No further approvals or
filings of any kind, including, without limitation, any further approvals of or
further filing with any governmental agency or other governmental authority, or
any approval of such Underwriter's board of directors or stockholders, are
necessary for this Agreement and the Underwriting Agreement to constitute the
legal, valid and binding obligation of such Underwriter.

          (d) Enforceability. This Agreement and the Underwriting Agreement will
each constitute a legal, valid and binding obligation of such Underwriter, each
enforceable in accordance with its terms, subject, as to the enforcement of
remedies, to bankruptcy, insolvency, reorganization, moratorium and other
similar laws affecting the enforceability of creditors' rights generally
applicable in the event of the bankruptcy, insolvency or reorganization of such
Underwriter and to general principles of equity.

                                       4

<PAGE>

          (e) No Litigation. There are no actions, suits, proceedings or
investigations pending or, to the best of such Underwriter's knowledge,
threatened against it at law or in equity or before any court, governmental
agency, board or commission or any arbitrator which, if decided adversely, would
materially and adversely affect its condition (financial or otherwise) or its
operations or would materially and adversely affect its ability to perform its
obligations under this Agreement and the Underwriting Agreement.

     Section 4. [Reserved.

     Section 5. Indemnification.

          (a) The Insurer hereby agrees, upon the terms and subject to the
conditions of this Agreement, to indemnify, defend and hold harmless each Issuer
Party and each Underwriter Party against (i) any and all Losses incurred by them
with respect to the offer and sale of any of the Offered Notes and resulting
from the Insurer's breach of any of its representations and warranties set forth
in Section 2 of this Agreement, and (ii) any and all Losses to which any Issuer
Party or any Underwriter Party may become subject, under the Act or otherwise,
subject to the limited scope of the Insurer Information described below insofar
as such Losses arise out of or result from an untrue statement of a material
fact contained in the Prospectus Supplement or the omission to state therein a
material fact required to be stated therein or necessary to make the statements
therein not misleading, in each case to the extent, but only to the extent, that
such untrue statement or omission was made in the Insurer Information included
therein; and provided further, that it is understood that the Insurer
Information is limited and does not purport to provide the scope of disclosure
required to be included in a prospectus for a registrant under the Securities
Act of 1933, in connection with the public offer and sale of securities of such
registrant.

          (b) Each Underwriter hereby agrees, severally and not jointly, upon
the terms and subject to the conditions of this Agreement, to indemnify, defend
and hold harmless each Insurer Party against (i) any and all Losses incurred by
it with respect to the offer and sale of any of the Offered Notes and resulting
from such Underwriter's breach of any of its agreements, representations and
warranties set forth in Section 3 of this Agreement and (ii) any and all Losses
to which any Insurer Party may become subject, under the Act or otherwise,
insofar as such Losses arise out of or result from an untrue statement of a
material fact contained in the Prospectus Supplement or the omission to state
therein a material fact required to be stated therein or necessary to make the
statements therein not misleading in each case to the extent, but only to the
extent, that such untrue statement or omission was made in the Underwriter
Information (as defined above) included therein.

          (c) Upon the incurrence of any Losses entitled to indemnification
hereunder, the Indemnifying Party shall reimburse the Indemnified Party promptly
upon establishment by the Indemnified Party to the Indemnifying Party of the
Losses incurred.

                                       5

<PAGE>

     Section 6. Notice To Be Given.

          (a) Except as provided in Section 7 below with respect to
contribution, the indemnification provided herein by the Indemnifying Party
shall be the exclusive remedy of each Indemnified Party for the Losses resulting
from the Indemnifying Party's breach of a representation, warranty or agreement
hereunder; provided, however, that each Indemnified Party shall be entitled to
pursue any other remedy at law or in equity for any such breach so long as the
damages sought to be recovered shall not exceed the Losses incurred thereby
resulting from such breach.

          (b) In the event that any action or regulatory proceeding shall be
commenced or claim asserted which may entitle an Indemnified Party to be
indemnified under this Agreement, such party shall give the Indemnifying Party
written or facsimile notice of such action or claim reasonably promptly after
receipt of written notice thereof.

          (c) Upon request of the Indemnified Party, the Indemnifying Party
shall retain counsel reasonably satisfactory to the Indemnified Party to
represent the Indemnified Party and any others the Indemnifying Party may
designate in such proceeding and shall pay the fees and disbursements of such
counsel related to such proceeding. The Indemnifying Party may, at its option,
at any time upon written notice to the Indemnified Party, assume the defense of
any proceeding and may designate counsel reasonably satisfactory to the
Indemnified Party in connection therewith, provided that the counsel so
designated would have no actual or potential conflict of interest in connection
with such representation. Unless it shall assume the defense of any proceeding,
the Indemnifying Party shall not be liable for any settlement of any proceeding,
effected without its written consent, but if settled with such consent or if
there be a final judgment for the plaintiff, the Indemnifying Party agrees to
indemnify the Indemnified Party from and against any loss or liability by reason
of such settlement or judgment. The Indemnifying Party shall be entitled to
participate in the defense of any such action or claim in reasonable cooperation
with, and with the reasonable cooperation of, each Indemnified Party.

          (d) The Indemnified Party will have the right to employ its own
counsel in any such action, but the fees and expenses of such counsel will be at
the expense of such Indemnified Party unless (i) the employment of counsel by
the Indemnified Party at the Indemnifying Party's expense has been authorized in
writing by the Indemnifying Party, (ii) the Indemnifying Party has not in fact
employed counsel to assume the defense of such action within a reasonable time
after receiving notice of the commencement of the action or (iii) the named
parties to any such action include the Indemnifying Party on the one hand and,
on the other hand, the Indemnified Party, and representation of both parties by
the same counsel would be inappropriate due to actual or potential differing
interests between them (in which case if such Indemnified Party notifies the
Indemnifying Party in writing that it elects to employ separate counsel at the
expense of the Indemnifying Party, the Indemnifying Party shall not have the
right to assume the defense of such action or proceeding on such Indemnified
Party's behalf), in each of which cases the reasonable

                                       6

<PAGE>

fees and expenses of counsel (including local counsel) will be at the expense of
the Indemnifying Party, and all such fees and expenses will be reimbursed
promptly as they are incurred. In the event that any expenses so paid by the
Indemnifying Party are subsequently determined not to be required to be borne by
the Indemnifying Party hereunder, the party which received such payment shall
promptly refund to the Indemnifying Party the amount so paid by such
Indemnifying Party. Notwithstanding the foregoing, in connection with any one
action or separate but substantially similar or related actions in the same
jurisdiction arising out of the same general allegations or circumstances, the
Indemnifying Party shall not be liable for the fees and expenses of more than
one counsel for the Issuer Parties, more than one counsel for all Underwriter
Parties and more than one counsel for all Insurer Parties, as applicable.

          (e) The Indemnified Parties shall cooperate with the Indemnifying
Parties in resolving any event, which would give rise to an indemnity obligation
pursuant to Section 5 hereof in the most efficient manner.

          (f) No settlement of any such claim or action shall be entered into
without the consent of each Indemnified Party who is subject to such claim or
action, on the one hand, and each Indemnifying Party who is subject to such
claim or action, on the other hand; provided, however, that the consent of such
Indemnified Party shall not be required if such settlement fully discharges,
with prejudice against the plaintiff, the claim or action against such
Indemnified Party.

          (g) Any failure by an Indemnified Party to comply with the provisions
of this Section shall relieve the Indemnifying Party of liability only if such
failure is materially prejudicial to any legal pleadings, grounds, defenses or
remedies in respect thereof or the Indemnifying Party's financial liability
hereunder, and then only to the extent of such prejudice.

     Section 7. Contribution.

          (a) To provide for just and equitable contribution if the
indemnification provided by the Insurer is determined to be unavailable for any
Underwriter Party (other than pursuant to Section 4 or 5 of this Agreement), or
if the indemnification provided by the Underwriters is determined to be
unavailable for any Insurer Party (other than pursuant to Section 4 or 6 of this
Agreement), the Insurer and the relevant Underwriter shall contribute to the
aggregate costs of liabilities arising from any breach of their respective
representations and warranties set forth in this Agreement on the basis of the
relative fault of all Insurer Parties and all relevant Underwriter Parties.

          (b) To provide for just and equitable contribution if the
indemnification provided by the Insurer is determined to be unavailable for the
Issuer Parties (other than pursuant to Section 5 or 6 of this Agreement), the
Insurer shall contribute to the aggregate cost of liabilities arising from any
breach of their respective representations and warranties set forth in this
Agreement on the basis of the relative fault of all Insurer Parties and the
Issuer Parties.

                                       7

<PAGE>

          (c) Notwithstanding anything in this Section 7 to the contrary, (i)
the Insurer shall not be required to contribute an amount in excess of the
amount by which the total of the insurance premiums that have been received by
the Insurer under the Insurance Agreement exceeds the amount of any damages that
the Insurer has otherwise been required to pay in respect of any breach by the
Insurer of the representations and warranties contained in Section 2 hereof, and
(ii) no Underwriter shall be required to contribute an amount in excess of the
amount by which the total underwriting fees, discounts and commissions received
by such Underwriter exceeds the amount of any damages that such Underwriter has
otherwise been required to pay in respect of any breach by such Underwriter of
its representations and warranties contained in Section 3 hereof.

          (d) The relative fault of each Indemnifying Party, on the one hand,
and of each Indemnified Party, on the other hand, shall be determined by
reference to, among other things, whether the breach of, or alleged breach of,
any of its representations and warranties set forth in Section 2 or 3 of this
Agreement relates to information supplied by, or action within the control of,
the Insurer Party or the relevant Underwriter Party and the Parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such breach.

          (e) The Parties agree that the Insurer shall be solely responsible for
the Insurer Information and for the Insurer Financial Statements, that each
Underwriter shall be responsible for the Underwriter Information provided by
such Underwriter in writing for use in the Prospectus Supplement.

          (f) No person guilty of fraudulent misrepresentation (within the
meaning of Section 11(f) of the Act) shall be entitled to contribution from any
person who was not guilty of such fraudulent misrepresentation.

          (g) The indemnity agreements contained in this Agreement shall remain
operative and in full force and effect, regardless of (i) any investigation made
by or on behalf of any Underwriter Party, any Insurer Party or any Issuer Party,
(ii) the issuance of any Offered Notes or the Policy or (iii) any termination of
this Agreement.

          (h) Upon the incurrence of any Losses entitled to contribution
hereunder, the contributor shall reimburse the party entitled to contribution
promptly upon establishment by the party entitled to contribution to the
contributor of the Losses incurred.

          (i) The Underwriters shall be severally and not jointly liable for any
contribution required by this Section 7.

     Section 8. Notices. All notices and other communications provided for under
this Agreement shall be addressed to the address set forth below as to each
party or at such other address as shall be designated by a party in a written
notice to the other party.

                                       8

<PAGE>

     If to the Insurer:      MBIA Insurance Corporation
                             113 King Street
                             Armonk, NY 10504
                             Attention: Insured Portfolio Management--Structured
                                        Finance (IPM-SF)

     If to the Issuer Parties:

                             Capital One Auto Finance, Inc.
                             8000 Jones Branch Drive
                             McLean, Virginia 22202
                             Facsimile: (703) 875-1389
                             Confirmation: (703) 875-1305

                             With a copy to Legal Department
                             Facsimile: (703) 875-1589
                             Confirmation: (703) 875-1000

                             Capital One Auto Receivables, LLC
                             8000 Jones Branch Drive
                             McLean, Virginia 22202
                             Facsimile: (703) 875-1389
                             Confirmation: (703) 875-1305

                             With a copy to Legal Department
                             Facsimile: (703) 875-1589
                             Confirmation: (703) 875-1000

     If to the Representative:

                             Credit Suisse First Boston Corporation
                             Eleven Madison Avenue
                             5/th/ Floor
                             New York, NY 10010-3629
                             Attention: General Counsel

     Section 9. Governing Law, Etc. This Agreement shall be deemed to be a
contract under the laws of the State of New York and shall be governed by and
construed in accordance with the laws of the State of New York without regard to
its conflicts of laws provisions. This Agreement may not be assigned by any
party without the express written consent of each other party. Amendments of
this Agreement shall be in writing signed by each party. This Agreement shall
not be effective until executed by each of the Insurer, each Issuer Party and
the Underwriters.

                                       9

<PAGE>

          Section 10. Other Obligations Not Effected. This Agreement in no way
limits or otherwise affects the indemnification obligations of the Underwriters
and COAF under the Underwriting Agreement.

          Section 11. Limitations. Nothing in this Agreement shall be construed
as a representation or undertaking by the Insurer concerning maintenance of the
rating currently assigned to its claims-paying ability by Moody's Investors
Service, Inc. ("Moody's") and/or Standard & Poor's, a division of The
McGraw-Hill Companies, Inc. ("S&P") or any other rating agency (collectively,
the "Rating Agencies").

          Section 12. Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall together
constitute but one and the same instrument.

          Section 13. Non-petition. So long as the Insurance Agreement is in
effect, and for one year following its termination, each of the parties hereto
agree that it (with respect to itself) file any involuntary petition or
otherwise institute any bankruptcy, reorganization, arrangement, insolvency or
liquidation proceeding or other proceeding under any federal or state bankruptcy
or similar law against the Issuer Parties or the Seller.

                                       10

<PAGE>

         IN WITNESS WHEREOF, the Parties hereto have caused this Indemnification
Agreement to be duly executed and delivered by their respective officers
thereunto duly authorized, all as of the date first above written.

                                   MBIA INSURANCE CORPORATION

                                   By   /s/ Amy R. Gonch
                                       -----------------------------------------
                                            Amy R. Gonch
                                   Title  Assistant Secretary
                                          --------------------------------------



                                   CREDIT SUISSE FIRST BOSTON
                                   CORPORATION, for itself and as Representative
                                   of the Underwriters

                                   By /s/ John L. McWilliams, IV
                                     -------------------------------------------
                                   Title  Director
                                         ---------------------------------------




                                   CAPITAL ONE AUTO FINANCE, INC., as Issuer
                                   Party

                                   By /s/ Jeffery Elswick
                                     -------------------------------------------
                                   Title  Manager of Securitization
                                         ---------------------------------------




                                   CAPITAL ONE AUTO RECEIVABLES, LLC, as Issuer
                                   Party

                                   By  /s/ Jeffery Elswick
                                     -------------------------------------------
                                   Title  President
                                         ---------------------------------------

<PAGE>

                               TABLE OF CONTENTS
<TABLE>
<CAPTION>
<S>                                                                             <C>
Section 1.    Definitions .....................................................  1
Section 2.    Representations and Warranties of the Insurer ...................  3
Section 3.    Representations and Warranties of the Underwriters...............  4
Section 4.    Reserved ........................................................  5
Section 5.    Indemnification .................................................  5
Section 6.    Notice To Be Given ..............................................  6
Section 7.    Contribution ....................................................  7
Section 8.    Notices .........................................................  8
Section 9.    Governing Law, Etc ..............................................  9
Section 10.   Other Obligations Not Effected .................................. 10
Section 11.   Limitations ..................................................... 10
Section 12.   Counterparts .................................................... 10
Section 13.   Non-petition .................................................... 10


TESTIMONIUM ....................................................... SIGNATURE PAGE

SIGNATURES ........................................................ SIGNATURE PAGE
</TABLE>