Document:

<PAGE>

                                                                     EXHIBIT 4.2

                            [FORM OF FACE OF NOTE]

          UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE
OF THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), TO THE COMPANY
OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY
CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME
AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE
TO CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED
REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER
HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

                        PROVIDIAN FINANCIAL CORPORATION

               3.25% Convertible Senior Note due August 15, 2005

     No. R-                                                     $_______________
     CUSIP No. 74406A AA 0

          PROVIDIAN FINANCIAL CORPORATION, a corporation duly organized and
existing under the laws of the State of Delaware (herein called the "Company",
which term includes any successor Person under the Indenture hereinafter
defined), for value received, hereby promises to pay to CEDE & CO., or
registered assigns, the principal sum of $___________  (____________ Dollars) on
August 15, 2005, and to pay interest thereon from August 23, 2000 or from the
most recent Interest Payment Date to which interest has been paid or duly
provided for, semi-annually on February 15 and August 15 in each year,
commencing February 15, 2001, at the rate of 3.25% per annum, until the
principal hereof is paid or made available for payment.

          The interest so payable, and punctually paid or duly provided for, on
any Interest Payment Date will, as provided in the Indenture, be paid to the
Person in whose name this Note is registered at the close of business on the
regular record date for such interest, which shall be the 1st of February or 1st
of August, as the case may be, next preceding such Interest Payment Date or, if
such record date is not a Business Day, at the close of business of the
immediately succeeding Business Day.  A "Business Day" shall mean any day other
than a Saturday, Sunday, a federally recognized holiday or a day on which
banking institutions are not authorized or required by law or executive order to
be open in the State of New York.  Any such interest not so punctually paid or
duly provided for will forthwith cease to be payable to the Holder on such
regular record date and shall be paid to the Person in whose name this Note is
registered at the close of business on a subsequent special record date, which
date shall be the fifteenth day next preceding the date fixed by the Company for
the payment of defaulted interest or the next succeeding Business Day if such
date is not a Business Day.  At least 15 days before the special record date,
the Company shall mail or cause to be mailed to each Holder, with a copy to the
Trustee, a notice that states the special record date, the payment date, and the
amount of
<PAGE>

defaulted interest, and interest payable on such defaulted interest, if any, to
be paid.

          Payments of principal of and interest on this Note and any additional
payments due hereunder shall be made at the office or agency of the Company
maintained for that purpose in the Borough of Manhattan, The City of New York,
in such coin or currency of the United States of America as at the time of
payment is legal tender for payment of public and private debts; provided,
however, that at the option of the Company payment of interest may be made by
check mailed to the address of the Person entitled thereto as such address shall
appear in the register for the Notes maintained by the Registrar.

          Reference is hereby made to the further provisions of this Note set
forth on the reverse hereof, which further provisions shall for all purposes
have the same effect as if set forth at this place.

          Unless the certificate of authentication hereon has been executed by
the Trustee referred to on the reverse hereof or an authenticating agent
appointed by the Company, by manual signature, this Note shall not be entitled
to any benefit under the Indenture or be valid or obligatory for any purpose.

                                       2
<PAGE>

          IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed and delivered under its corporate seal.

     Dated:

                              PROVIDIAN FINANCIAL CORPORATION

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

          This is one of the Securities of the Series designated therein
referred to in the within-mentioned Indenture.

     Dated:

                              BANK ONE TRUST COMPANY, N.A.,
                              as Trustee

                              By:
                                 ---------------------------------------------
                                             Authorized Signatory

                                       3
<PAGE>

                           [FORM OF REVERSE OF NOTE]

          This Note is one of a duly authorized issue of securities of the
Company (herein called the "Notes"), issued and to be issued in one or more
series under an Indenture, dated as of May 1, 1999 (as supplemented by a First
Supplemental Indenture, dated as of August 23, 2000, the "Indenture"), between
the Company and Bank One Trust Company, N.A., as Trustee (herein called the
"Trustee", which term includes any successor trustee under the Indenture), and
reference is hereby made to the Indenture for a statement of the respective
rights, limitations of rights, duties and immunities thereunder of the Company,
the Trustee, and the Holders of the Notes and of the terms upon which the Notes
are, and are to be, authenticated and delivered.  This Note is one of the series
designated on the face hereof as "3.25% Convertible Senior Notes due August 15,
2005", limited in aggregate principal amount to $402,500,000.  All terms used in
this Note which are defined in the Indenture shall have the meanings assigned to
them in the Indenture.

          The Notes are subject to redemption, at the election of the Company,
at any time on or after August 20, 2003, as a whole or in part, upon not less
than 30 nor more than 60 days' notice to the Holders (in the manner provided for
in the Indenture) prior to the Redemption Date at the following redemption
prices (expressed as percentages of the principal amount):

<TABLE>
<CAPTION>
     Redemption Date                                 Redemption Price:
     ---------------                                 -----------------
     <S>                                             <C>
     from August 20, 2003 until August 14, 2004            101.30%
     from August 15, 2004 until Stated Maturity            100.65%
</TABLE>

together in each case of any such redemption with accrued interest to the
Redemption Date; provided, however, that interest installments whose payment
date is on or prior to such Redemption Date will be payable to the Holders of
such Notes of record at the close of business on the relevant Record Dates
referred to on the face hereof, all as provided in the Indenture.

          No sinking fund is provided for the Notes.

          Subject to and upon compliance with the provisions of the Indenture,
any Note (or any portion of the principal amount thereof which is $1,000 or an
integral multiple of $1,000) which has not previously been redeemed or
repurchased, is convertible at the option of the Holder thereof, at any time
following the original issue date of the Notes and on or before the close of
business on the Business Day immediately preceding the Stated Maturity, into
fully paid and nonassessable shares of common stock of the Company, $0.01 par
value per share (the "Common Stock"), at an initial conversion rate (calculated
to the nearest 1/100 of a share) of 7.2446 shares of Common Stock for each
$1,000 principal amount of Note, or at the current adjusted conversion rate if
an adjustment has been made as provided in the Indenture.  In case the Notes or
a portion thereof are called for redemption, such conversion right in respect of
the Notes or portion so called shall expire at the close of business on the
Business Day immediately preceding the Redemption Date, unless the Company
defaults in making the payment due upon redemption.  A Note or portion thereof
in respect of which the Holder has delivered a Repurchase Notice may be
converted only if such notice is withdrawn in accordance with the

                                       4
<PAGE>

terms of the Indenture, unless the Company has defaulted in the payment of the
Change of Control Purchase Price. The Holder of a Note surrendered for
conversion during the period from the close of business on any Record Date
immediately preceding any Interest Payment Date to the opening of business on
such Interest Payment Date shall (except in the case of a Note or portions
thereof which have been called for redemption or in respect of which the
Repurchase Notice delivered by the Holder has not been withdrawn, the conversion
rights of which would terminate during the period between such Record Date and
the close of business on such Interest Payment Date) be entitled to receive the
interest payable on such Interest Payment Date on the principal amount of the
Note being surrendered for conversion. To convert this Note the Holder must (1)
surrender this Note, duly endorsed or assigned to the Company or in blank,
provided that if such surrender shall be made during the period from the close
of business on any Record Date immediately preceding any Interest Payment Date
to the opening of business on such Interest Payment Date shall (except in the
case of Notes or portions thereof which have been called for redemption or in
respect of which the Repurchase Notice delivered by the Holder has not been
withdrawn, the conversion rights of which would terminate during the period
between such Record Date and the close of business on such Interest Payment
Date) also be accompanied by payment in immediately available funds or other
funds acceptable to the Company of an amount equal to the interest payable on
such Interest Payment Date on the principal amount of the Note being surrendered
for conversion, and (2) complete and manually sign a conversion notice in
substantially the form attached hereto. Except as set forth above, no payment or
adjustment shall be made upon any conversion on account of any interest accrued
hereon from the Interest Payment Date immediately preceding the day of
conversion, or on account of any dividends on the Common Stock issued on
conversion hereof. In addition, the Holders shall not be entitled to receive any
dividends payable to holders of Common Stock as of any record date before the
close of business on the conversion date. No fractional shares will be issued on
conversion, but instead of any fractional interest (calculated to the nearest
1/100th of a share) the Company shall pay a cash adjustment as provided in the
Indenture.

          The Indenture provides that in the event of any merger, amalgamation,
arrangement or consolidation to which the Company is a party (other than one
that does not result in any reclassification, conversion, exchange or
cancellation of the Common Stock) or any conveyance, lease, sale or transfer of
all or substantially all of the assets of the Company, the Indenture shall be
amended, without the consent of any Holders of Notes, so that this Note, if then
outstanding, will be convertible thereafter, during the period this Note shall
be convertible as specified above, only into the kind and amount of securities,
cash and other property receivable upon such merger, amalgamation, arrangement,
consolidation, conveyance, lease, sale or transfer by a holder of the number of
shares of Common Stock of the Company into which this Note could have been
converted immediately prior to such merger, amalgamation, arrangement,
consolidation, conveyance, lease, sale or transfer (assuming such holder of
Common Stock is not a Constituent Person or an Affiliate of a Constituent
Person, failed to exercise any rights of election and received per share the
kind and amount received per share by a plurality of Non-Electing Shares).  No
adjustment in the Conversion Rate shall be made until such adjustment would
require an increase or decrease of at least one percent of such rate, provided
that any adjustment that would otherwise be made will be carried forward and
taken into account in the computation of any subsequent adjustment.

          Subject to and upon compliance with the provisions of the Indenture,
upon the

                                       5
<PAGE>

occurrence of a Change of Control, the Company shall notify the Holders of the
Notes of such occurrence by delivering a Change of Control Notice, shall make a
Change of Control Offer and shall purchase, on a Business Day not more than 60
nor less than 30 days following the Change of Control Date (a "Change of Control
Purchase Date") all of the then outstanding Notes validly tendered at a purchase
price in cash equal to 100% of the principal amount thereof plus accrued
interest, if any, to the Change of Control Purchase Date (the "Change of Control
Purchase Price"). The Change of Control Offer shall remain open from the time of
delivery of the Change of Control Notice for at least 20 Business Days and until
5:00 p.m., New York City time, on the Business Day prior to the Change of
Control Purchase Date. To exercise its repurchase right, a Holder shall deliver
to the Trustee a Repurchase Notice, in accordance with the terms and conditions
set forth in the Change of Control Notice. Upon receipt by the Trustee of a
Repurchase Notice, the Holder of the Note in respect of which such Repurchase
Notice was given shall (unless such Repurchase Notice is withdrawn) thereafter
be entitled to receive solely the Change of Control Purchase Price with respect
to such Note and, unless the Company has defaulted in the payment of the Change
of Control Purchase Price, any Note accepted for payment pursuant to the Change
of Control Offer shall cease to accrue interest after the Change of Control
Purchase Date. Holders of Notes will be entitled to withdraw their election if
the Paying Agent receives notice of such withdrawal not later than 5:00 p.m.,
New York City time, on the Business Day prior to the Change of Control Purchase
Date. Notes in respect of which a Repurchase Notice has been given by the Holder
thereof may not be converted into shares of Common Stock on or after the date of
the delivery of such Repurchase Notice, unless such Repurchase Notice has first
been validly withdrawn in the manner provided for in the Indenture or unless the
Company has defaulted in the payment of the Change of Control Purchase Price.
Holders electing to have Notes purchased pursuant to a Change of Control Offer
will be required to surrender their Notes to the Paying Agent at the address (in
the Borough of Manhattan, The City of New York) specified in the Change of
Control Notice prior to 5:00 p.m., New York City time, on the Business Day prior
to the Change of Control Purchase Date and must complete any form of letter of
transmittal proposed by the Company and reasonably acceptable to the Trustee and
the Paying Agent. Any portion of the principal amount of Notes that is equal to
$1,000 or an integral multiple thereof, validly tendered into the Change of
Control Offer and not withdrawn, will be accepted for payment.

          In the event of redemption, repurchase or conversion of this Note in
part only, a new Note or Notes for the unredeemed, unrepurchased or unconverted
portion hereof will be issued in the name of the Holder hereof upon the
cancellation thereof.

          The provisions for defeasance and covenant defeasance set forth in
Sections 1302 and 1303 of the Indenture, respectively, will not apply to the
Notes.

          If an Event of Default with respect to the Notes shall occur and be
continuing, the principal of all the Notes may be declared due and payable in
the manner and with the effect provided in the Indenture.

          The Indenture permits, with certain exceptions as therein provided,
the amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Notes under the Indenture at any
time by the Company and the Trustee with the consent of the Holders of 66 2/3%
in principal amount of the Notes at the time

                                       6
<PAGE>

Outstanding. The Indenture also contains provisions permitting the Holders of a
majority in principal amount of the Notes at the time Outstanding, on behalf of
the Holders of all Notes, to waive compliance by the Company with certain
provisions of the Indenture and certain past defaults under the Indenture and
their consequences. Any such consent or waiver by the Holder of this Note shall
be conclusive and binding upon such Holder and upon all future Holders of this
Note and of any Note issued upon the registration of transfer hereof or in
exchange herefor or in lieu hereof, whether or not notation of such consent or
waiver is made upon this Note.

          As provided in and subject to the provisions of the Indenture, the
Holder of this Note shall not have the right to institute any proceeding with
respect to the Indenture or for the appointment of a receiver or trustee or for
any other remedy thereunder, unless such Holder shall have previously given the
Trustee written notice of a continuing Event of Default with respect to the
Notes, the Holders of not less than 25% in principal amount of the Notes at the
time Outstanding shall have made written request to the Trustee to institute
proceedings in respect of such Event of Default as Trustee and offered the
Trustee reasonable indemnity, and the Trustee shall not have received from the
Holders of a majority in principal amount of the Notes at the time Outstanding a
direction inconsistent with such request, and shall have failed to institute any
such proceeding, for 60 days after receipt of such notice, request and offer of
indemnity.  The foregoing shall not apply to any suit instituted by the Holder
of this Note for the enforcement of any payment of principal hereof or any
premium or interest hereon on or after the respective due dates expressed herein
or for the enforcement of the right to convert this Note as provided in the
Indenture.

          No reference herein to the Indenture and no provision of this Note or
of the Indenture shall alter or impair the obligation of the Company, which is
absolute and unconditional, to pay the principal of and any premium and interest
on this Note at the times, place and rate, and in the coin or currency, herein
prescribed or to convert this Note as provided in the Indenture.

          As provided in the Indenture and subject to certain limitations
therein set forth, the transfer of this Note is registrable in the Security
Register, upon surrender of this Note for registration of transfer at the office
or agency of the Company in any place where the principal of and any premium and
interest on this Note are payable, duly endorsed by, or accompanied by a written
instrument of transfer in form satisfactory to the Company and the Security
Registrar duly executed by, the Holder hereof or such Holder's attorney duly
authorized in writing, and thereupon one or more new Notes, of authorized
denominations and for the same aggregate principal amount, will be issued to the
designated transferee or transferees.

          This Note is a Global Note and shall be exchangeable for Notes
registered in the names of Persons other than the Depositary with respect to
this Global Note or its nominee only if (A) such Depositary notifies the Company
that it is unwilling or unable to continue as Depositary for this Global Note or
at any time ceases to be a clearing agency registered as such under the
Securities Exchange Act of 1934, as amended, (B) the Company in its discretion
executes and delivers to the Trustee a Company Order that this Global Note shall
be exchangeable or (C) there shall have occurred and be continuing an Event of
Default with respect to the Notes.  If this Global Note is exchangeable pursuant
to the preceding sentence, it shall be exchangeable for Notes issuable in
denominations of $1,000 and any integral multiple of

                                       7
<PAGE>

$1,000 in excess thereof, registered in such names as such Depositary shall
direct.

          The Notes are issuable only in registered form without coupons in
denominations of $1,000 and any integral multiple thereof.  As provided in the
Indenture and subject to certain limitations therein set forth, the Notes are
exchangeable for a like aggregate principal amount of Notes of a different
authorized denomination, as requested by the Holder surrendering the same.

          No service charge shall be made for any such registration of transfer
or exchange, but the Company may require payment of a sum sufficient to cover
any tax or other governmental charge payable in connection therewith.

          Prior to due presentment of this Note for registration of transfer,
the Company, the Trustee and any agent of the Company or the Trustee may treat
the Person in whose name this Note is registered as the owner hereof for all
purposes, whether or not this Note be overdue, and neither the Company, the
Trustee nor any such agent shall be affected by notice to the contrary.

          A director, officer, employee, stockholder or incorporator, as such,
of the Company shall not have any liability (except in the case of bad faith or
willful misconduct) for any obligations of the Company under the Notes or the
Indenture or for any claim based on, in respect of or by reason of such
obligations or their creations.  Each Holder by accepting a Note waives and
releases all such liability.  Such waiver and release are part of the
consideration for the issuance of the Notes.

          THE INDENTURE AND THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED IN
ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, AS APPLIED TO CONTRACTS MADE
AND PERFORMED WITHIN THE STATE OF NEW YORK WITHOUT REGARD TO PRINCIPLES OF
CONFLICTS OF LAW.

          All terms used in this Note which are defined in the Indenture shall
have the meanings assigned to them in the Indenture.

                                       8
<PAGE>

                                 ABBREVIATIONS

          The following abbreviations, when used in the inscription on the face
of this Note, shall be construed as though they were written out in full
according to applicable laws or regulations:

<TABLE>
<CAPTION>
          <S>                         <C>
          TEN COM               -     as tenants in common

          TEN ENT               -     as tenants by the entireties (Cust)

          JT TEN                -     as joint tenants with right of
                                      survivorship and not as tenants in common

          UNIF GIFT MIN ACT     -     Uniform Gifts to Minors Act
</TABLE>

          Additional abbreviations may also be used though not in the above
list.

                                       9
<PAGE>

                               CONVERSION NOTICE

          The undersigned Holder of this Note hereby irrevocably exercises the
option to convert this Note, or any portion of the principal amount hereof
(which is $1,000 in principal amount or an integral multiple of $1,000), below
designated, into shares of common stock of Providian Financial Corporation,
$0.01 par value per share (the "Common Stock"), in accordance with the terms of
the Indenture referred to in this Note, and directs that such shares, together
with a check in payment for any fractional share and any Notes representing any
unconverted portion of the principal amount hereof, be issued and delivered to
and be registered in the name of the undersigned unless a different name has
been indicated below.  If shares of Common Stock or any portion of this Note not
converted are to be registered in the name of a Person other than the
undersigned, (a) the undersigned will pay all transfer taxes payable with
respect thereto and (b) signature(s) must be guaranteed by an Eligible Guarantor
Institution with membership in an approved signature guarantee program pursuant
to Rule 17Ad-15 under the Securities Exchange Act of 1934.

     Dated _________________

                                 ______________________________________________

                                 ______________________________________________
                                                   Signature(s)

     If shares or Notes are to be registered in the name of a Person other than
     the Holder, please print such Person's name and address:

     ____________________________________
                    Name

     ____________________________________
                  Address

     ____________________________________
     Social Security or Other Taxpayer
     Identification Number

     ____________________________________
     [Signature Guaranteed]

                                       10
<PAGE>

     If only a portion of the Notes is to be converted, please indicate:

1.   Principal amount to be converted:

          $__________________

2.   Principal amount and denomination of Notes representing unconverted
     principal amount to be issued:

          $__________________

                                       11
<PAGE>

                   ELECTION OF HOLDER TO REQUIRE REPURCHASE
                           UPON A CHANGE OF CONTROL

          (1) Pursuant to Article 4 of the First Supplemental Indenture dated as
of August 23, 2000 to the Indenture, the undersigned hereby acknowledges receipt
of a notice from the Company of a Change of Control Offer and requests and
instructs the Company to repurchase this Note, or the portion hereof (which is
$1,000 in principal amount or an integral multiple of $1,000) below designated,
as of the Change of Control Purchase Date pursuant to the terms and conditions
specified in such Article 4.

          (2) The undersigned hereby directs the Trustee or the Company to pay
to the undersigned an amount in cash equal to 100% of the principal amount to be
repurchased (as set forth below), plus interest accrued to the Change of Control
Purchase Date, as provided in the Indenture.

          (3) The undersigned elects (check one):

          ( ) to receive the Change of Control Purchase Price with respect to
the following portions of the following Notes:

              Note certificate number:

              Principal amount to be repurchased (if less than all):
$___________________

              Remaining principal amount after repurchase:  $___________________

          ( ) to receive the Change of Control Purchase Price with respect to
the full principal amount of all of the Notes that are subject to this notice.

Notice:  If the Holder fails to make an election, the Holder shall be deemed to
have elected to receive the Change of Control Purchase Price for the full
principal amount of all of the Notes subject to this notice.

Dated ________________

____________________________________

____________________________________

                                       12
<PAGE>

                                               Signature(s)

                              Signature(s) must be guaranteed by an Eligible
                              Guarantor Institution with membership in an
                              approved signature guarantee program pursuant to
                              Rule 17Ad-15 under the Securities Exchange Act of
                              1934.

____________________________________
      Signature Guaranteed

                              Security certificate number:

                              Principal amount to be repurchased
                              (if less than all):  $_____________________

                              Remaining principal amount after
                              repurchase:
                              $_____________________

                              ____________________________________
                              Social Security or Other Taxpayer
                              Identification Number

                                       13
<PAGE>

                              FORM OF ASSIGNMENT

          For value received ________________ hereby sell(s), assign(s) and
transfer(s) unto ________________ [also insert social security or other taxpayer
identification number of assignee] the within Note, and hereby irrevocably
constitutes and appoints ____________________ as attorney to transfer the said
Note on the books of the Company, with full power of substitution in the
premises.

     Dated _________________

                              _______________________________________________

                              _______________________________________________

                              Signature(s)

                              Signature(s) must be guaranteed by an Eligible
                              Guarantor Institution with membership in an
                              approved signature guarantee program pursuant to
                              Rule 17Ad-15 under the Securities Exchange Act of
                              1934.

                                       14<PAGE>   1

                                                                     EXHIBIT 4.2

NUMBER                                                                    SHARES

     1                                                                    100

                     INCORPORATED UNDER THE LAWS OF BERMUDA

                              TRENWICK GROUP LTD.
                        PAR VALUE OF SHARES US$0.10 EACH

     THIS IS TO CERTIFY THAT [               ], [               ] IS THE
REGISTERED HOLDER OF ONE HUNDRED FULLY PAID COMMON SHARES OF THE PAR VALUE OF US
$0.10 EACH IN THE ABOVE-NAMED COMPANY, SUBJECT TO THE MEMORANDUM OF ASSOCIATION
AND BYE-LAWS THEREOF.

     GIVEN UNDER THE COMMON SEAL OF THE COMPANY THIS [  ] DAY OF [          ],
2000.

                                          SPECIMEN CERTIFICATE

                                 -------------------------------------- DIRECTOR

                                -------------------------------------- SECRETARY

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