<PAGE>
                                                                    EXHIBIT 10.2

                              EXCHANGE AGREEMENT

          This Exchange Agreement ("Agreement") is made this 9th day of March,
2001 by and among Pride International, Inc., a Louisiana corporation (the
"Company"), First Reserve Fund VIII, L.P., a Delaware limited partnership (the
"Fund VIII"), and First Reserve Fund VII, Limited Partnership, a Delaware
limited partnership (the "Fund VII" and, together with Fund VIII, "First
Reserve").

                                   RECITALS:

          WHEREAS, the Company and Fund VIII entered into the Securities
Purchase Agreement dated as of May 5, 1999, as amended by the Letter Agreements
dated June 4, 1999, June 18, 1999, June 21, 1999 and July 14, 1999 and by the
Put and Exchange Agreement dated September 14, 1999 (as so amended, the
"Purchase Agreement");

          WHEREAS, pursuant to the Purchase Agreement and the Subscription
Agreement, dated as of September 14, 1999, among Amethyst Financial Company
Limited, a British Virgin Islands corporation ("Amethyst"), Drillpetro Inc., a
Bahamian corporation ("Drillpetro"), Techdrill Inc., a Bahamian corporation
("Techdrill"), Westville Management Corporation, a British Virgin Islands
corporation ("Westville"), Fund VIII and Fund VII, First Reserve purchased an
aggregate of 1,250 shares of common stock, par value $1.00 per share, of
Amethyst ("Amethyst Common Stock").  Pursuant to the Purchase Agreement, First
Reserve acquired a right to exchange the Amethyst Common Stock for an aggregate
of 1,047,120 shares of the Company's common stock, no par value per share (the
"Company Common Stock");

          WHEREAS, the Company, Fund VIII and Fund VII entered into the First
Amended and Restated Shareholders Agreement dated as of March 31, 2000 (the
"Shareholders Agreement");

          WHEREAS, pursuant to the Master Restructuring Agreement, dated as of
March 9, 2001 (the "Master Agreement"), among the Company, Drillpetro,
Techdrill, Fund VII, Fund VIII, Maritima Petroleo e Engenharia Ltda., a
Brazilian limited liability company, Westville, Amethyst and Pride Amethyst II
Ltd., a British Virgin Islands company ("Amethyst II"), Amethyst is to
distribute to First Reserve an aggregate of 1,250 common shares, par value $1.00
per share ("Amethyst II Stock"), of the capital stock of Amethyst II; and

          WHEREAS, pursuant to the Master Agreement, the Company and First
Reserve desire to amend the Purchase Agreement to provide that (i) the Amethyst
II Stock shall constitute Exchangeable Stock within the meaning of the Purchase
Agreement, (ii) the Company Common Stock into which the Amethyst Common Stock
and the Amethyst II Stock can be exchanged pursuant to the Purchase Agreement
shall equal an aggregate of 519,468 and 527,652 shares of Company Common Stock,
respectively, (iii) at the Closing (as defined in the Master Agreement), First
Reserve shall exchange its shares of Amethyst Common Stock for an aggregate of
519,468 shares of Company Common Stock and (iv) First Reserve shall continue to
have the exchange rights as set forth in the Purchase Agreement, as clarified by
this Agreement, with respect to the Amethyst II Stock distributed to it pursuant
to the Master Agreement;
<PAGE>

          NOW, THEREFORE, in consideration of the premises, the mutual promises
made herein and other good and valuable consideration, the receipt of which is
hereby acknowledged, the parties hereto do hereby agree as follows:

          Section 1. Amendment; Meanings of Certain Terms. This Agreement
constitutes an amendment to the Purchase Agreement and to the Shareholders
Agreement. From and after the Closing, (i) the Amethyst II Stock distributed to
Fund VIII and Fund VII (or to another member of First Reserve Group) pursuant to
the Master Agreement constitutes the "Exchangeable Stock" under the Purchase
Agreement and the Shareholders Agreement and shall be exchangeable for an
aggregate of 527,652 shares of Common Stock as set forth in the Purchase
Agreement and this Agreement, (ii) all references to "Amethyst" in the
definition of "Exchangeable Stock" in Section 1.1 of the Purchase Agreement and
in Section 5.10 of the Purchase Agreement shall be to Amethyst II, (iii) all
references to the "Amethyst Agreement" in the Purchase Agreement and the
Shareholders Agreement shall be to the Put and Exchange Agreement dated
September 14, 1999 between the Company and Fund VIII, as amended by this
Agreement, and (iv) for purposes of Section 5.11 of the Purchase Agreement, the
"Exchangeable Stock Purchase Price" shall be calculated as if First Reserve had
initially invested $6,298,851 on the Closing Date. Capitalized terms used herein
that are not otherwise defined shall have the respective meanings given them in
the Purchase Agreement.

          Section 2. Exchange of Amethyst Common Stock. At the Closing, (i) Fund
VIII shall surrender to the Company the 1,100 shares of Amethyst Common Stock
held of record by Fund VIII, (ii) Fund VII shall surrender to the Company the
150 shares of Amethyst Common Stock held of record by Fund VII, (iii) the
corresponding right to exchange such shares of Amethyst Common Stock for Common
Stock shall be cancelled, and (iv) the Company shall issue to Fund VIII and Fund
VII 457,132 shares and 62,336 shares of Common Stock, respectively. The 1,250
shares of Amethyst Common Stock so surrendered by First Reserve represent all
the capital stock of Amethyst beneficially owned by any member of the First
Reserve Group. Such surrender shall be (i) in cancellation of the exchange
rights of First Reserve with respect to the Amethyst Common Stock set forth in
Section 5.10 of the Purchase Agreement, as adjusted to take into account the
issuance of the Amethyst II Stock, and (ii) otherwise effected in accordance
with paragraphs (i) through (iv) of Section 5.10.

          Section 3. Representations and Warranties of First Reserve. First
Reserve hereby represents and warrants to the Company as follows:

                (a) Valid Title. Each of Fund VIII and Fund VII has valid title
          to the shares of Amethyst Common Stock to be exchanged by such fund
          pursuant to Section 2 hereof, free and clear of any security interest,
          mortgage, pledge, lien, charge, claim, equity or encumbrance of any
          kind; and upon delivery of such shares of Amethyst Common Stock in
          exchange for the shares of Common Stock pursuant to Section 2 hereof,
          assuming the Company has no notice of any adverse claim, the Company
          will receive valid title to such shares of Amethyst Common Stock, free
          and clear of any security interest, mortgage, pledge, lien, charge,
          claim, equity or encumbrance of any kind.

                (b) Securities Laws. Each of Fund VIII and Fund VII is an
          "accredited investor" as such term is defined in Rule 501 under the
          Securities Act. Each of Fund VIII
<PAGE>

          and Fund VII (i) has such knowledge and experience in financial and
          business matters as enables it to evaluate the merits and risks of an
          investment in the shares of Common Stock issuable upon exchange of the
          Amethyst Common Stock and the Amethyst II Stock pursuant to the
          Purchase Agreement and this Agreement (the "Company Shares") and (ii)
          is acquiring such Company Shares for its own account and not with the
          view to resale or redistribution thereof in violation of the
          Securities Act; provided, however, that each of Fund VIII and Fund VII
          shall at all times retain full power and authority over the transfer
          of its properties and assets. Each of Fund VIII and Fund VII
          acknowledges that it may not transfer the Company Shares except
          pursuant to an effective registration statement under the Securities
          Act or pursuant to an exemption from the registration requirements of
          the Securities Act, and that a legend to such effect shall be included
          on any certificate representing the Company Shares.

          Section 4. Counterparts; Facsimile. This Agreement may be executed in
any number of counterparts, each of which when so executed shall be deemed an
original but all of which together shall constitute one and the same instrument.
This Agreement may be delivered by delivery of facsimile signature pages.

          Section 5. Ratification; Confirmation. Except to the extent otherwise
expressly contemplated hereby, the Purchase Agreement is hereby ratified and
confirmed.

          Section 6. Exercise of Rights. Any right provided for in this
Agreement may be exercised by the party possessing such right by notice in
writing given to all of the other parties to this Agreement, which notice shall
state the right being exercised.

          Section 7. Notice. Notice required or permitted under this Agreement
shall be deemed to be given two days after a writing thereof is deposited in the
United States mail, return receipt requested, addressed to the address for each
party set forth below or such other address as such party may fix by notice
similarly given:

          To the Company:

          Pride International, Inc.
          5847 San Felipe, Suite 3300
          Houston, Texas 77057
          Fax:  713-789-1430
          Attn: Mr. Paul A. Bragg
                President and Chief Executive Officer

          with a copy to:

          Baker Botts L.L.P.
          910 Louisiana
          Houston, Texas 77002
          Fax: 713-229-1522
          Attn: L.P. Thomas, Esq.
<PAGE>

          If  to First Reserve:

          First Reserve Fund VIII, L.P.
          c/o First Reserve Corp.
          1801 California Street
          Denver, Colorado 80202
          Fax: 303-382-1275
          Attn: Thomas Denison, Esq.

          With a copy to:

          Gibson, Dunn & Crutcher LLP
          1801 California, Suite 4100
          Denver, Colorado 80202
          Fax: 303-313-2839
          Attn: Beau Stark

          Section 8. Binding Effect. This Agreement shall be binding upon and
inure to the benefit of the parties hereto and their respective successors and
assigns. First Reserve will not assign its rights under this Agreement or
transfer or dispose of any shares of Exchangeable Stock unless the assignee or
transferee agrees to be bound by the Purchase Agreement and this Agreement.

          Section 9. Governing Law. This Agreement shall be governed by, and
construed in accordance with, the laws of the State of New York applicable to
agreements made and performed wholly in the State of New York.

          Section 10. Severability. If any provision or this Agreement shall be
held invalid, such invalidity shall not affect any other provision of this
Agreement that can be given effect without the invalid provision, and to this
end, the provisions hereof are separable.

          Section 11. Headings. The headings in this Agreement are for reference
purposes only and shall not affect in any way the meaning or interpretation of
this Agreement.

          Section 12. Amendment. This Agreement cannot be amended or modified
except by a written agreement executed by the parties hereto.
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first written above.

                                       PRIDE INTERNATIONAL, INC.


                                       By: /s/ ROBERT W. RANDALL
                                          ________________________________
                                          Name: Robert W. Randall
                                          Title:

                                       FIRST RESERVE FUND VIII, L.P.

                                       By: First Reserve GP VIII, L.P.,
                                           its General Partner

                                       By: First Reserve Corporation,
                                           its General Partner


                                       By: /s/ THOMAS R. DENISON
                                          ________________________________
                                          Thomas R.  Denison
                                          Managing Director

                                       FIRST RESERVE FUND VII, LIMITED
                                       PARTNERSHIP

                                       By: First Reserve GP VII, L.P.,
                                           its General Partner

                                       By: First Reserve Corporation,
                                           its General Partner


                                       By: /s/ THOMAS R. DENISON
                                          ________________________________
                                          Thomas R.  Denison
                                          Managing Director