<PAGE>   1
                                                                    Exhibit 4.20



                                  AMENDMENT TO

                               GUARANTEE AGREEMENT

                                       OF

                              PWG Capital Trust II



                         Dated as of December 22, 2000



<PAGE>   2
                  AMENDMENT dated as of December 22, 2000 ("Amendment") to the
GUARANTEE AGREEMENT of PWG Capital Trust II, between UBS Americas Inc. (as
successor by merger to Paine Webber Group Inc. ("PaineWebber")), as guarantor
(the "Guarantor"), and The Chase Manhattan Bank, a New York banking corporation,
as guarantee trustee (the "Guarantee Trustee"), dated as of March 14, 1997 (the
"Guarantee Agreement") for the benefit of the Holders from time to time of the
Preferred Securities of PWG Capital Trust II (the "Issuer").

                             RECITALS OF THE COMPANY

                  Pursuant to the Third Supplemental Indenture, dated as of
November 3, 2000, between PaineWebber and UBS Americas Inc. (the "Guarantor"),
the Guarantor succeeded to the obligations of PaineWebber under the Guarantee
Agreement.

                  The Guarantor has requested the Guarantee Trustee and the
Parent Guarantor to join with it in the execution and delivery of this amendment
(the "Amendment") in order to supplement and amend the Guarantee Agreement, by
amending and adding certain provisions thereof, to allow the Guarantor to accept
the Parent Guarantor's guarantee of the Guarantor's obligations under the
Guarantee Agreement.

                  The Guarantor is a wholly owned subsidiary of the Parent
Guarantor, and the Parent Guarantor wishes to guarantee, on a subordinated
basis, the Guarantor's obligations pursuant to the Guarantee Agreement.

                  The Parent Guarantor has authorized the execution and delivery
of this Amendment by a resolution of or under the authority of its board of
directors.

                  Section 9.02 of the Guarantee Agreement provides that the
Guarantee Agreement may be amended without the consent of any Holders of the
Preferred Securities of the Issuer, provided such action does not adversely
affect the interests of the Holders of the Preferred Securities of the Issuer.

                  The Guarantor has determined that the execution and delivery
of this Amendment by the Guarantor, the Parent Guarantor and the Guarantee
Trustee complies with said Section 9.02 and does not require the consent of any
Holder of the Preferred Securities of the Issuer.

                  At the request of the Guarantee Trustee, the Guarantor has
furnished the Guarantee Trustee with an Opinion of Counsel complying with the
requirements of Section 2.05 of the Guarantee Agreement, stating, among
<PAGE>   3
other things, that the execution of this Amendment is authorized or permitted by
the Guarantee Agreement.

                  All conditions and requirements necessary to make this
Amendment a valid agreement of the Guarantor, in accordance with the terms of
the Guarantee Agreement, and a valid amendment of and supplement to the
Guarantee Agreement have been done.

                  NOW THEREFORE, the Guarantor, the Parent Guarantor and the
Guarantee Trustee hereby agree as follows:

                  1. Section 1.01 of the Guarantee Agreement is hereby amended
by the insertion of the following definition:

                     "Parent Guarantor" means UBS AG, a Swiss banking
              corporation, until a successor Person shall have become such
              pursuant to the applicable provisions of this Guarantee Agreement
              and thereafter "Parent Guarantor" shall mean such Person.

                  2. The Guarantee Agreement is hereby amended by the insertion
of the following Article Five-A after the existing Article Five:

                                 ARTICLE FIVE-A

                              The Parent Guarantee

Section 5.01-A. Unconditional Guarantee; Subordination.

                  For value received, the Parent Guarantor hereby
unconditionally and irrevocably guarantees, as a primary obligor and not merely
as a surety, all of the obligations of the Guarantor under this Guarantee
Agreement, regardless of any defense, right of set-off or counterclaim that the
Issuer may have or assert.

                  The Parent Guarantor hereby agrees that this guarantee is an
absolute, present and continuing guarantee of payment and not of collectability
and that its obligations hereunder shall be unconditional, irrespective of the
validity, legality or enforceability of the Guarantee Agreement.

                  This guarantee shall bind the Parent Guarantor and its
successors and assigns. This guarantee constitutes a direct, unconditional and
unsecured obligation of the Parent
<PAGE>   4
Guarantor. The obligations of the Parent Guarantor hereunder will be
subordinated in right of payment to the prior payment in full of the deposit
liabilities of the Parent Guarantor and all other liabilities of the Parent
Guarantor (including all deposit liabilities and other liabilities of the head
office and all offices of the Parent Guarantor wherever located), except (i) any
liabilities which by their terms rank pari passu with or are subordinated to the
obligations of the Parent Guarantor under this guarantee; (ii) any Existing Pari
Passu Obligations (as defined in the Indenture); (iii) any liabilities which by
their terms rank pari passu with or are subordinated to liabilities which by
their terms rank pari passu with or are subordinated to the obligations of the
Parent Guarantor under this guarantee or any Existing Pari Passu Obligations;
and (iv) any Existing Junior Subordinated Obligations (as defined under the
Indenture). For the avoidance of doubt, (A) the obligations of the Parent
Guarantor hereunder will rank pari passu with any Existing Pari Passu
Obligations and any liabilities which by their terms rank pari passu with this
guarantee or any Existing Pari Passu Obligations; and (B) the obligations of the
Parent Guarantor hereunder will be senior to any Existing Junior Subordinated
Obligations and any liabilities which by their terms are subordinated to the
obligations of the Parent Guarantor under this guarantee or under any Existing
Pari Passu Obligations.

                  3. Section 9.03 is hereby amended by the insertion of the
following subsection (d):

                     (d) if given to the Parent Guarantor, to the address set
              forth below or such other address as the Parent Guarantor may give
              notice of to the Holders:

                       UBS AG
                       Bahnhofstrasse 45, Zurich
                       Switzerland
                       Facsimile No.:
                       Attention: General Counsel

                  4. The Guarantee Agreement is hereby amended by the insertion
of the following paragraphs at the end of Article IX:

Section 9.09.  Successors and Assigns of the Parent Guarantor.

<PAGE>   5
                  All guarantees and agreements contained in the Guarantee
Agreement shall bind the successors, assignees, receivers, trustees and
representatives of the Parent Guarantor and shall inure to the benefit of the
Holders of the Preferred Securities then outstanding. Except in connection with
a consolidation, merger or conveyance, transfer or lease of assets involving the
Parent Guarantor under Article Ten of the Indenture, the Parent Guarantor shall
not assign its obligations hereunder.

                  5. Ratification and Confirmation. As amended and modified by
this Amendment, the Guarantee Agreement is in all respects ratified and
confirmed and the Guarantee Agreement and this Amendment shall be read, taken
and construed as one and the same instrument.

                  6. Counterparts. This Amendment may be executed in any number
of counterparts and all said counterparts executed and delivered each as an
original shall constitute but one and the same instrument.

                  7. Trustee's Duties, Responsibilities and Liabilities. The
Trustee assumes no duties, responsibilities or liabilities by reason of this
Amendment other than as set forth in the Amendment, and this Amendment is
executed and accepted by the Trustee subject to all the terms and conditions of
their acceptance of the trust under the Guarantee Agreement, as fully as if said
terms and conditions were herein set forth at length.

<PAGE>   6
                  This Amendment is executed as of the day and year first above
written.

                                        UBS AMERICAS INC. (as
                                        successor by merger to
                                        Paine Webber Group Inc.)



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



                                        UBS AG



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




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



                                        THE CHASE MANHATTAN BANK, as
                                        Guarantee Trustee



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