<PAGE>

                                                                  [Exhibit 10.9]

          FIRST SUPPLEMENTAL INDENTURE, dated as of September 15, 2006 (this
"Supplemental Indenture"), between VALIDUS HOLDINGS, LTD., a company with
limited liability organized under the laws of Bermuda (the "Company"), and
JPMORGAN CHASE BANK, NATIONAL ASSOCIATION, a national banking association, as
Trustee (in such capacity, the "Trustee").

                                   WITNESSETH

          REFERENCE is made to the Indenture, dated as of June 15, 2006 (the
"Original Indenture" and as amended and modified by this Supplemental Indenture,
the "Indenture"), between the Company and the Trustee, pursuant to which the
Company issued its Junior Subordinated Deferrable Interest Debentures due 2036.
Capitalized terms used but not defined herein shall have the meaning ascribed to
such terms in the Indenture.

          WHEREAS, the Company has requested that the Trustee enter into this
Supplemental Indenture to amend certain provisions of the Original Indenture;

          WHEREAS, Section 9.2 of the Original Indenture provides that with the
consent of the Holders of not less than a majority in aggregate principal amount
of the Outstanding Securities, by Act of said Holders delivered to the Company
and the Trustee, the Company, when authorized by a Board Resolution, and the
Trustee may enter into an indenture supplemental thereto for the purpose of
(subject to certain limited exceptions) adding any provisions to or changing in
any manner or eliminating any of the provisions of the Original Indenture or of
modifying in any manner the rights of the Holders of Securities;

          WHEREAS, all necessary actions for the execution and delivery of this
Supplemental Indenture have been taken pursuant to Article IX of the Indenture
and the Trustee has received an Officers' Certificate and Opinion of Counsel,
stating, among other things, that the execution of this Supplemental Indenture
is authorized or permitted by the Original Indenture and that all conditions
precedent therein have been complied with, each as contemplated by Section 9.3
of the Indenture in connection with the execution and delivery of this
Supplemental Indenture;

     WHEREAS, the Trustee has provided a copy of this Supplemental Indenture to
the Holders and the Company has obtained the Consent of not less than a majority
of aggregate principal amount of the Outstanding Securities to such Supplemental
Indenture; and

          WHEREAS, all things necessary to make this Supplemental Indenture a
valid agreement of the Company, in accordance with its terms, have been done.

          NOW, THEREFORE, for and in consideration of the premises and the
mutual covenants and agreements hereinafter contained and for other good and
valuable consideration, the receipt and adequacy of which is hereby
acknowledged, the undersigned parties hereto agree, for the equal and
proportionate benefit of the Holders, as follows:

<PAGE>

                                    ARTICLE I

                                   AMENDMENTS

          SECTION 1.1 Section 1.1 of the Indenture is hereby amended by
inserting the following defined terms in such Section in alphabetical order:

     "Closing Date" shall mean June 15, 2006.

     "Fixed Rate Period" shall mean the period beginning on the Closing Date
     through but excluding June 15, 2011.

          SECTION 1.2 The form of Security set forth in Section 2.1 of the
Indenture is hereby amended by deleting the first sentence of the second
paragraph thereof and replacing said sentence with the following:

     "The amount of interest payable for any interest period shall be computed
     and paid (i) during the Fixed Rate Period on the basis of a 360-day year of
     twelve 30-day months and (ii) thereafter on the basis of a 360-day year and
     the actual number of days elapsed in the relevant interest period."

          SECTION 1.3 Section 3.1(d) of the Indenture is hereby amended by
deleting such Section in its entirety and replacing such Section with the
following:

     "(d) Payments of interest on the Securities shall include interest accrued
     to but excluding the respective Interest Payment Dates. Interest payments
     for the Securities shall be computed and paid (i) during the Fixed Rate
     Period on the basis of a 360-day year of twelve 30-day months and (ii)
     thereafter on the basis of a 360-day year and the actual number of days
     elapsed in the relevant interest period."

                                   ARTICLE II

                                  MISCELLANEOUS

          SECTION 2.1 Successors and Assigns.

          This Supplemental Indenture shall be binding upon and shall inure to
the benefit of any successor to the Company and the Trustee, including any
successor by operation of law.

          SECTION 2.2 Separability Clause.

          If any provision in this Supplemental Indenture or in the Securities
shall be invalid, illegal or unenforceable, the validity, legality and
enforceability of the remaining provisions shall not in any way be affected or
impaired thereby, and there shall be deemed substituted for the provision at
issue a valid, legal and enforceable provision as similar as possible to the
provision at issue.


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<PAGE>

          SECTION 2.3 Governing Law.

          THIS SUPPLEMENTAL INDENTURE AND THE RIGHTS AND OBLIGATIONS OF EACH OF
THE HOLDERS, THE COMPANY AND THE TRUSTEE SHALL BE CONSTRUED AND ENFORCED IN
ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK WITHOUT
REFERENCE TO ITS CONFLICT OF LAWS PROVISIONS (OTHER THAN SECTION 5-1401 OF THE
GENERAL OBLIGATIONS LAW).

                                     * * * *

          This instrument may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but all such counterparts
shall together constitute but one and the same instrument.

                                     * * * *


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<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the day and year first above written.

                                        VALIDUS HOLDINGS, LTD.


                                        By:
                                            ------------------------------------
                                        Name:
                                              ----------------------------------
                                        Title:
                                               ---------------------------------


                                        JPMORGAN CHASE BANK, NATIONAL
                                        ASSOCIATION, as Trustee


                                        By:
                                            ------------------------------------
                                        Name:
                                              ----------------------------------
                                        Title:
                                               ---------------------------------


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