CERTIFICATE GUARANTY INSURANCE POLICY ENDORSEMENT

EXHIBIT 4.5

Ambac Assurance Corporation (Ambac), a Wisconsin stock insurance corporation, in consideration of the payment of the premium and subject to the terms of this Policy, hereby agrees unconditionally and irrevocably to pay to the Trustee for the benefit of the Holders of the Insured Obligations, that portion of the Insured Amounts which shall become Due for Payment but shall be unpaid by reason of Nonpayment.

Ambac will make such payments to the Trustee from its own funds on the later of (a) one (1) Business Day following notification to Ambac of Nonpayment or (b) the Business Day on which the Insured Amounts are Due for Payment. Such payments of principal or interest shall be made only upon presentation of an instrument of assignment in form and substance satisfactory to Ambac, transferring to Ambac all rights under such Insured Obligations to receive the principal of and interest on the Insured Obligation. Ambac shall be subrogated to all the Holders’ rights to payment on the Insured Obligations to the extent of the insurance disbursements so made. Once payments of the Insured Amounts have been made to the Trustee, Ambac shall have no further obligation hereunder in respect of such Insured Amounts.

In the event the Trustee for the Insured Obligations has notice that any payment of principal or interest on an Insured Obligation which has become Due for Payment and which is made to a Holder by or on behalf of the Trustee has been deemed a preferential transfer and theretofore recovered from its Holder pursuant to the United States Bankruptcy Code in accordance with a final, nonappealable order of a court of competent jurisdiction, such Holder will be entitled to payment from Ambac to the extent of such recovery if sufficient funds are not otherwise available.

This Policy is noncancelable by Ambac for any reason, including failure to receive payment of any premium due hereunder. The premium on this Policy is not refundable for any reason. This Policy does not insure against loss of any prepayment or other acceleration payment which at any time may become due in respect of any Insured Obligation, other than at the sole option of Ambac, nor against any risk other than Nonpayment, including failure of the Trustee to make any payment due Holders of Insured Amounts.

To the fullest extent permitted by applicable law, Ambac hereby waives and agrees not to assert any and all rights and defenses, to the extent such rights and defenses may be available to Ambac, to avoid payment of its obligations under this Policy in accordance with the express provisions hereof.

Any capitalized terms not defined herein shall have the meaning given such terms in the endorsement attached hereto or in the Agreement.

In witness whereof, Ambac has caused this Policy to be affixed with its corporate seal and to be signed by its duly authorized officers in facsimile to become effective as their original signatures and binding upon Ambac by virtue of the countersignature of its duly authorized representative.

CERTIFICATE GUARANTY INSURANCE POLICY ENDORSEMENT

For all purposes of the Policy, the following terms shall have the following meanings:

“Agreements” shall mean, for purposes of the Policy, the Indenture and the Servicing Agreement.

“Available Funds” shall have the meaning assigned to such term in the Indenture.

“Business Day” shall mean any day other than (i) a Saturday or Sunday, (ii) a day on which banking institutions in the state of New York, the state of California or the state in which the Corporate Trust Office is located are required or authorized by law or executive order to be closed or (iii) a day on which the Insurer is closed.

“Deficiency Amount” means with respect to the Notes, the sum of (i) for any Payment Date the excess, if any, of (a) the Interest Payment Amount (excluding any Deferred Interest) over (b) the portion of the Available Funds for such Payment Date remaining after payment of the Indenture Trustee Fee, the Premium Amount, the Credit Risk Manager Fee and the Owner Trustee Fee, in each case, for such Payment Date, such portion being (x) during the Managed Amortization Period, the pro rata portion of such remaining Available Funds based on the pari passu application of such amount to the Interest Payment Amount and to interest on any Additional Balance Contributed Amount at the Note Rate on such Payment Date and (y) after the Managed Amortization Period, all such remaining Available Funds, (ii) for any Payment Date other than the Final Scheduled Payment Date, the Overcollateralization Deficit, if any, for such Payment Date remaining after giving effect to payments pursuant to Section 8.7(b)(viii) of the Indenture on such Payment Date and (iii) on the Final Scheduled Payment Date, the Outstanding Amount of the Notes, after taking into account all payments to be made to the Notes on the Final Scheduled Payment Date other than pursuant to the Policy.

“Due for Payment” shall mean, (i) with respect to an Insured Amount, the Payment Date on which Insured Amounts are due and payable pursuant to the terms of the Indenture and (ii) with respect to a Preference Amount, the Business Day on which the documentation required by the Insurer has been received by the Insurer.

“Final Scheduled Payment Date” shall mean the Payment Date occurring in August 2030.

“First Payment Date” shall mean the Payment Date occurring in October 2004.

“Holder” shall mean the registered owner or beneficial owner of any Note, but shall not include the Issuer, the Indenture Trustee, the Owner Trustee, the Servicer, the Sellers or the Sponsor.

“Indenture” shall mean the Indenture between the Issuer and the Indenture Trustee, dated August 1, 2004, as such agreement may be amended, modified or supplemented from time to time.

“Indenture Trustee” shall mean U.S. Bank National Association or its successor-in-interest, in its capacity as Indenture Trustee under the Indenture, or if any successor trustee or any co-trustee shall be appointed as provided therein, then “Indenture Trustee” shall also mean such successor trustee or such co-trustee, as the case may be, subject to the provisions thereof.

“Insurance Agreement” shall mean the Insurance and Indemnity Agreement, dated as of September 10, 2004, among GreenPoint Mortgage Securities LLC, as Sponsor, GreenPoint Mortgage Funding, Inc., as Servicer, U.S. Bank National Association, as Indenture Trustee, the Insurer, and GreenPoint Home Equity Loan Trust 2004-4, as Issuer, as such agreement may be amended, modified or supplemented from time to time.

“Insured Amounts” shall mean, with respect to any Payment Date and the Notes, the Deficiency Amount for such Payment Date.

“Insured Payments” shall mean, with respect to any Payment Date, the aggregate amount actually paid by the Insurer to the Indenture Trustee in respect of (i) Insured Amounts for a Payment Date and (ii) Preference Amounts for any given Business Day.

“Insurer” shall mean Ambac Assurance Corporation, or any successor thereto, as issuer of the Policy.

“Issuer” shall mean GreenPoint Home Equity Loan Trust 2004-4.

“Late Payment Rate” shall mean for any Payment Date, the lesser of (i) the greater of (a) the rate of interest, as it is publicly announced by Citibank, N.A. at its principal office in New York, New York as its prime rate (any change in such prime rate of interest to be effective on the date such change is announced by Citibank, N.A.) plus 2% and (b) the then applicable highest rate of interest on the Notes and (ii) the maximum rate permissible under applicable usury or similar laws limiting interest rates. The Late Payment Rate shall be computed on the basis of the actual number of days elapsed over a year of 360 days.

“Nonpayment” shall mean, with respect to any Payment Date, an Insured Amount is Due for Payment but has not been paid pursuant to the Indenture.

“Notes” shall mean the GreenPoint Home Equity Loan Trust 2004-4, Class A Variable Rate Asset-Backed Notes, substantially in the form set forth in Exhibit A to the Indenture.

“Notice” shall mean the telephonic or telegraphic notice, promptly confirmed in writing by telecopy substantially in the form of Exhibit A to the Policy, the original of which is subsequently delivered by registered or certified mail, from the Indenture Trustee specifying the

Insured Amount or Preference Amount which shall be due and owing on the applicable Payment Date.

“Payment Date” shall mean the 15th day of each month, or if such day is not a Business Day, then the next Business Day, beginning with the First Payment Date.

“Policy” shall mean Certificate Guaranty Insurance Policy AB0794BE together with each and every endorsement thereto.

“Preference Amount” shall mean any payment of principal or interest previously distributed to a Holder on a Note, which would have been covered under the Policy as an Insured Amount, which has been deemed a preferential transfer and was previously recovered from its owner pursuant to the United States Bankruptcy Code in accordance with a final, non-appealable order a court of competent jurisdiction.

“Premium” shall mean the amount payable to the Insurer on each Payment Date calculated at the Premium Percentage.

“Premium Percentage” shall have the meaning set forth in the Insurance Agreement.

“Reimbursement Amount” shall mean, as to any Payment Date, the sum of (x) (i) all Insured Payments paid by the Insurer, but for which the Insurer has not been reimbursed prior to such Payment Date pursuant to Section 8.7(b)(ix) of the Indenture, plus (ii) interest accrued on such Insured Payments not previously repaid, calculated at the Late Payment Rate from the date the Indenture Trustee received the related Insured Payments, and (y) without duplication (i) any amounts then due and owing to the Insurer under the Insurance Agreement, as certified to the Indenture Trustee by the Insurer plus (ii) interest on such amounts at the Late Payment Rate.

“Relief Act Shortfalls” shall mean interest shortfalls resulting from the application of the Servicemembers Relief Act, as amended, or any similar state law.

“Servicing Agreement” shall mean the Sale and Servicing Agreement, dated as of August 1, 2004 among GreenPoint Mortgage Securities LLC, as Sponsor, GreenPoint Mortgage Funding, Inc., as Servicer and Seller, Terwin Advisors LLC, as Seller, the Indenture Trustee, The Murrayhill Company, as Credit Risk Manager, and the Issuer, as such agreement may be amended, modified or supplemented from time to time.

“Trust Agreement” shall mean the Trust Agreement, dated as of August 1, 2004, between GreenPoint Mortgage Securities Inc., as Sponsor and Wilmington Trust Company, as Owner Trustee, as such agreement may be amended, modified or supplemented from time to time.

Capitalized terms used herein as defined terms and not otherwise defined herein shall have the meaning assigned to them in the Insurance Agreement and the Agreements, without regard to any amendment or modification thereof, unless such amendment or modification has been approved in writing by the Insurer.

Notwithstanding any other provision of the Policy, the Insurer will pay any Insured Amount payable hereunder no later than 12:00 noon, New York City time, on the later of (i) the

Payment Date on which the related Insured Amount is Due for Payment and (ii) the third Business Day following receipt in New York, New York on a Business Day by the Insurer of a Notice at the address and in the manner provided in Section 6.02 of the Insurance Agreement; provided that, if such Notice is received after 12:00 noon, New York City time, on such Business Day, it shall be deemed to be received on the following Business Day. If any such Notice is not in proper form or is otherwise insufficient for the purpose of making a claim under the Policy, it shall be deemed not to have been received for purposes of this paragraph, and the Insurer shall promptly so advise the Indenture Trustee and the Indenture Trustee may submit an amended or corrected Notice.

The Insurer will pay any Preference Amount when due to be paid pursuant to the Order (as defined below), but in any event no earlier than the third Business Day following receipt by the Insurer of (i) a certified copy of a final, non-appealable order of a court or other body exercising jurisdiction in such insolvency proceeding to the effect that the Indenture Trustee, or Holder, as applicable, is required to return such Preference Amount paid during the term of the Policy because such payments were avoided as a preferential transfer or otherwise rescinded or required to be restored by the Indenture Trustee or Holder (the “Order”), (ii) a certificate by or on behalf of the Indenture Trustee or Holder that the Order has been entered and is not subject to any stay, (iii) an assignment, in form and substance satisfactory to the Insurer, duly executed and delivered by the Indenture Trustee or Holder, irrevocably assigning to the Insurer all rights and claims of the Indenture Trustee or Holder relating to or arising under the Indenture and the Servicing Agreement against the estate of the Indenture Trustee or otherwise with respect to such Preference Amount and (iv) a Notice (in the form attached hereto as Exhibit A) appropriately completed and executed by the Indenture Trustee; provided, that if such documents are received after 12:00 noon, New York City time, on such Business Day, they will be deemed to be received on the following Business Day; provided, further, that the Insurer shall not be obligated to make any payment in respect of any Preference Amount representing a payment of principal on the Notes prior to the time the Insurer would have been required to make a payment in respect of such principal pursuant to the first paragraph of the face of the Policy. Such payment shall be disbursed to the receiver, conservator, debtor-in-possession or trustee in bankruptcy named in the Order, and not to the Holder directly, unless the Holder has made a payment of the Preference Amount to the court or such receiver, conservator, debtor-in-possession or trustee in bankruptcy named in the Order, in which case the Insurer will pay the Holder, subject to the delivery of (a) the items referred to in clauses (i), (ii), (iii) and (iv) above to the Insurer and (b) evidence satisfactory to the Insurer that payment has been made to such court or receiver, conservator, debtor-in-possession or trustee in bankruptcy named in the Order.

The Insurer shall be subrogated to the rights of each Holder to the extent of any payment by the Insurer under the Policy.

The Insurer hereby agrees that if it shall be subrogated to the rights of Holders by virtue of any payment under the Policy, no recovery of such payment will occur unless the full amount of the Holders’ allocable distributions for such Payment Date can be made. In so doing, the Insurer does not waive its rights to seek full payment of all Reimbursement Amounts owed to it under the Insurance Agreement and Agreements.

The Policy does not cover Deferred Interest, Relief Act Shortfalls or interest shortfalls due to the partial or full prepayment of the Mortgage Loans, nor does the Policy guarantee to the Holders of the Notes any particular rate of principal payment. In addition, the Policy does not cover shortfalls, if any, attributable to the liability of the Issuer, the Indenture Trustee or any Noteholder for withholding taxes, if any, (including interest and penalties in respect of any liability for withholding taxes) or any risk other than Nonpayment, including the failure of the Indenture Trustee to make any payment required under the Indenture to the Note holders.

The terms and provisions of the Indenture constitute the instrument of assignment referred to in the second paragraph of the face of the Policy.

A premium will be payable on the Policy on each Payment Date as provided in Section 8.7(b)(ii) of the Indenture, beginning with the First Payment Date, in an amount equal to the Premium.

THE INSURANCE PROVIDED BY THE POLICY IS NOT COVERED BY THE PROPERTY/CASUALTY INSURANCE SECURITY FUND SPECIFIED IN ARTICLE 76 OF THE NEW YORK INSURANCE LAWS.

The Policy to which this endorsement is attached and of which it forms a part is hereby amended to provide that there shall be no acceleration payment due under the Policy unless such acceleration is at the sole option of the Insurer.

Nothing herein contained shall be held to vary, alter, waive or extend any of the terms, conditions, provisions, agreements or limitations of the above mentioned Policy other than as above stated.

To the extent the provisions of this endorsement conflict with the provisions in the above-mentioned Policy, the provisions of this endorsement shall govern.

The Policy and the obligations of the Insurer thereunder will terminate without any action on the part of the Insurer or any other person on the date that is one year and one day following the earlier to occur of (i) the date on which all amounts required to be paid on the Notes have been paid in full and (ii) the Final Scheduled Payment Date. Upon termination of the Policy, the Indenture Trustee shall deliver the original of the Policy to the Insurer.

No person other than the Indenture Trustee shall be entitled to present the Notice.

No waiver of any rights or powers of the Insurer, the Holders or the Indenture Trustee or consent by any of them shall be valid unless signed by an authorized officer or agent thereof.

The Policy is issued under and pursuant to, and shall be construed in accordance with, the laws of the State of New York, without giving effect to the conflict of laws principles thereof.

IN WITNESS WHEREOF, Ambac Assurance Corporation has caused this endorsement to the Policy to be signed by its duly authorized officers

EXHIBIT A

TO THE CERTIFICATE GUARANTY INSURANCE POLICY

Policy No. AB0794BE

NOTICE OF NONPAYMENT AND DEMAND

FOR PAYMENT OF INSURED AMOUNTS

Date: [                    ]

Ambac Assurance Corporation

One State Street Plaza

New York, New York 10004

Attention: General Counsel

Reference is made to Certificate Guaranty Insurance Policy No. AB0794BE (the “Policy”) issued by Ambac Assurance Corporation (“Ambac”). Terms capitalized herein and not otherwise defined shall have the meanings specified in the Policy and the Indenture, dated as of August 1, 2004, between GreenPoint Home Equity Loan Trust 2004-4, as Issuer and U.S. Bank National Association, as Indenture Trustee, as the case may be, unless the context otherwise requires.

The Indenture Trustee hereby certifies as follows:

                                                                  (Indenture Trustee’s account number).

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ANY PERSON WHO KNOWINGLY AND WITH INTENT TO DEFRAUD ANY INSURANCE COMPANY OR OTHER PERSON FILES AN APPLICATION FOR INSURANCE OR STATEMENT OF CLAIM CONTAINING ANY MATERIALLY FALSE INFORMATION, OR CONCEALS FOR THE PURPOSE OF MISLEADING, INFORMATION CONCERNING ANY FACT MATERIAL THERETO, COMMITS A FRAUDULENT INSURANCE ACT, WHICH IS A CRIME AND SHALL ALSO BE SUBJECT TO A CIVIL PENALTY NOT TO EXCEED FIVE THOUSAND DOLLARS AND THE STATED VALUE OF THE CLAIM FOR EACH SUCH VIOLATION.

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