<PAGE>

                                                                    Exhibit 10.2
                                                                       (premium)

                      NONQUALIFIED STOCK OPTION AGREEMENT
                      -----------------------------------

                  1999 Incentive Plan of Pure Resources, Inc.

     This Option Agreement ("Agreement"), made and entered into effective as of
December 13, 1999, by and between Pure Resources, Inc., a Delaware corporation
(the "Company"), and [See Schedule 1 attached hereto] (the "Optionee").

                                  WITNESSETH:

     WHEREAS, the 1999 Incentive Plan of Pure Resources, Inc. (formerly named
Titan Resources Holdings, Inc.) ("Plan") was adopted by the Company, effective
as of December 13, 1999 ("Plan Date"), for the benefit of certain employees of
the Company and its subsidiaries; and

     WHEREAS, the Optionee is eligible to participate in the Plan and the
Committee has authorized the grant to Optionee of an option to purchase shares
of Common Stock, par value $0.01, of the Company ("Shares") pursuant to the Plan
and upon the terms set forth herein;

     NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements hereinafter set forth, the Company and Optionee hereby
agree as follows:

     1.   Certain Definitions.  Terms used in this Agreement and not otherwise
          -------------------
defined shall have the respective meanings assigned to such terms in the Plan;
and the following terms shall have the following meanings:

          Companies means the Company and any of its Subsidiaries (as defined in
          ---------
          the Plan).

          Expiration Date means 6:00 p.m., Midland, Texas time, on December 13,
          ---------------
          2009.

          Merger means the consummation of the merger of TRH, Inc. with into
          ------
          Titan pursuant to the terms of the Agreement and Plan of Merger dated
          as of December 13, 1999, by and among Union Oil Company of California,
          a California corporation, the Company, TRH, Inc., a Delaware
          corporation, and Titan.

          Premium Exercise Price means an amount equal to (a) 1.25 times the
          ----------------------
          average closing prices for a share of Titan common stock for each of
          the ten trading days prior to the consummation of the Merger, divided
          by (b) .4302314.

          Titan means Titan Exploration, Inc., a Delaware corporation.
          -----

     2.   Grant of Option. Subject to the terms, conditions and provisions of
          ---------------
the Plan and those hereinafter set forth, the Company hereby grants to Optionee
a Nonqualified Stock Option (the "Option") to purchase [See Schedule 1 attached
hereto] Shares, subject to adjustment in accordance with the provisions of
Section 7 of this Agreement.

     3.   Option Price.  The price to be paid by Optionee to the Company for
          ------------
each Share purchased pursuant to the exercise of this Option (the "Option
Price") shall be $17.08, which is the Premium Exercise
<PAGE>

Price per share; provided, however, that the Option Price shall be subject to
adjustment in accordance with the provisions of Section 7 of this Agreement.

     4.   Vesting of Right to Exercise Option.
          -----------------------------------

     (a)  Except as otherwise provided in this Agreement, the right to exercise
this Option shall vest in the manner set forth on Exhibit A, which is attached
hereto and incorporated herein by reference for all purposes.  From and after
each date of vesting, Optionee may exercise this Option, subject to the terms
and conditions set forth herein, to purchase all or any portion of the Shares
for which Optionee's rights have vested.

     (b)  To the extent Optionee does not purchase all or any part of the Shares
at the times this Option becomes exercisable, the Optionee has the right
cumulatively thereafter to purchase any Shares not so purchased and such right
shall continue until this Option terminates or expires.

     (c)  If Optionee's employment by the Companies is terminated on account of
fraud against the Company or a Subsidiary or conviction of a felony, the Option
shall automatically terminate as of the date of such termination of employment.

     (d)  If Optionee's employment by the Companies is terminated voluntarily by
Optionee or by action of the Companies for reasons other than as specified in
subsection (c), this Option may be exercised, but only (i) within three months
after such termination (if otherwise prior to the date of expiration of this
Option), and not thereafter, and (ii) to purchase the number of Shares, if any,
that could be purchased upon exercise of this Option at the date of termination
of Optionee's employment. For purposes of this subsection (d), if this Option
shall not have fully vested as of the date of Optionee's termination of
employment by action of the Companies for reasons other than as specified in
subsection (c) (but not in the event of voluntary termination), then a ratable
portion of the number of Shares which would have become purchasable upon the
next vesting date shall be deemed to have vested as of the date of such
termination (determined by multiplying the number of Shares that vest on the
next vesting date by a fraction with a numerator equal to the number of full
months which have then elapsed since the last vesting date and a denominator of
12, and rounding to the nearest whole number).

     (e)  In the event of Optionee's termination of employment with the
Companies by reason of death or disability (within the meaning of Section
22(e)(3) of the Code), this Option may be exercised by the person who acquires
this Option by will or the laws of descent and distribution, or by Optionee (or
the Optionee's legal guardian in the event one is appointed as a result of
Optionee's disability), as the case may be, but only (i) within the one year
period following the date of death or disability (if otherwise prior to the date
of expiration of this Option), and not thereafter, and (ii) to purchase the
number of Shares, if any, that could be purchased upon exercise of this Option
at the date of Optionee's death or disability. For purposes of this subsection
(e), if this Option shall not have fully vested as of the date of termination of
Optionee's employment, then a ratable portion of the number of Shares which
would have become purchasable upon the next vesting date shall be deemed to have
vested as of the date of such termination (determined by multiplying the number
of Shares that vest on the next vesting date by a fraction with a numerator
equal to the number of full months which have then elapsed since the last
vesting date and a denominator of 12, and rounding to the nearest whole number).

     5.   Restrictions on Exercise.  The right to exercise the Option shall be
          ------------------------
subject to the following restrictions:

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<PAGE>

     (a)  Vesting.  Optionee shall have no right to exercise this Option to
          -------
purchase any Shares for which Optionee's rights have not yet vested in
accordance with Section 4.

     (b)  No Fractional Shares. The Option may be exercised only with respect to
          --------------------
full Shares.

     (c)  Compliance with Law.  The Option may not be exercised in whole or in
          -------------------
part, and no Shares shall be issued nor certificates representing such Shares
(if any) delivered pursuant to any exercise of the Option, if any requisite
approval or consent of any governmental authority of any kind having
jurisdiction over the exercise of options or the issuance and sale of Shares
shall not have been obtained or if such exercise or issuance would violate any
applicable law.

     (d)  Exercise by Optionee.  The Option shall only be exercisable by the
          --------------------
Optionee and by any transferee who has received such Option pursuant to Section
4(e).

     6.   Exercise of Option.
          ------------------

     (a)  Subject to the other terms and provisions of this Agreement and the
Plan, the Option shall be exercisable by written notice timely given to the
Company by the Optionee (the "Exercise Notice"), which notice (i) shall state
the number of Shares that the Optionee then desires to purchase, and (ii) shall
be accompanied by payment in full of the Option Price for each of such Shares.
Unless the Company and Optionee shall have made mutually acceptable alternative
arrangements, payment of the Option Price shall be made in cash or by surrender
of previously acquired nonforfeitable, unrestricted Shares owned by the Optionee
(the "Payment Shares") having an aggregate Fair Market Value at the time of
exercise equal to the Option Price.

     (b)  Payment of the total Option Price may also be made, in the discretion
of the Committee, by delivery to the Company or its designated agent of an
executed irrevocable option exercise form together with irrevocable instructions
to a broker-dealer to sell or margin a sufficient portion of the Shares with
respect to which the Option is exercised and deliver the sale or margin loan
proceeds directly to the Company to pay the Option Price and any required
federal, state and local taxes.

     (c)  The Committee, in its sole and absolute discretion, may approve the
extension of a loan to Optionee by the Company to assist Optionee in paying the
exercise price of an Option and/or any tax required by law to be withheld upon
exercise of the Option; provided, however, that Optionee shall be required to
pay in cash the par value of Common Stock received upon exercise of the Option.
Any loan approved by the Committee shall be made upon such terms and conditions
(including interest rate, security and terms of repayment) as may be determined
by the Committee in its discretion.

     (d)  Unless the Company and Optionee shall make mutually acceptable
alternative arrangements, at the time of exercise of the Option, Optionee shall
pay to the Company any federal, state and local taxes required by law to be paid
or withheld in connection with such exercise.  The Company may require Optionee
to pay to the Company such taxes prior to and as a condition of the issuance or
delivery of the Shares and the Company or a Subsidiary shall be entitled to
deduct from any other compensation payable to the Participant any tax
withholding obligations with respect to the Option.

     7.   Recapitalization or Reorganization; Adjustments.
          -----------------------------------------------

     (a)  The existence of this Option shall not affect in any way the right or
power of the Company to make or authorize any adjustment, recapitalization,
reorganization or other change in the Company's capital

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<PAGE>

structure or its business, any merger or consolidation of the Company, any
issuance of additional securities by the Company with priority over Shares or
otherwise affecting Shares or the rights thereof, the dissolution or liquidation
of the Company or any sale, lease, exchange or other disposition of all or any
part of its assets or business or any other corporate act or proceeding.

     (b)  If (i) the Company enters into any merger, consolidation or
recapitalization pursuant to which the persons serving as directors of the
Company immediately before such transaction cease to constitute at least 40% of
the members of the board of directors of the surviving entity (whether the
Company or another entity) following consummation of such transaction, (ii) the
Company sells, leases or exchanges or agrees to sell, lease or exchange all or
substantially all of its assets to any other person or entity, or (iii) the
Company is to be dissolved and liquidated (each such event is referred to herein
as a "Fundamental Change"), then immediately before the consummation of the
Fundamental Change, any portion of the Option which has not then vested shall
become vested and the Company, at its discretion, shall either (x) provide to
Optionee at least 30 days' notice of such pending Fundamental Change so as to
permit Optionee to exercise the Option before consummation of such Fundamental
Change, in which case the Company need no make provision for this Option to
survive the consummation of such Fundamental Change, or (y) make or cause to be
made lawful and adequate provision whereby, upon the due exercise of this Option
after the effective date of such Fundamental Change, the Optionee shall be
entitled to purchase upon exercise of this Option, the number and class of
shares or other securities or property to which the Optionee would have been
entitled pursuant to the terms of the Fundamental Change if, immediately before
consummation of such Fundamental Change, Optionee had been the holder of record
of the number of Shares which could be purchased upon exercise of this Option
immediately before such Fundamental Change.

     (c)  If the Company subdivides its outstanding Shares into a greater number
of Shares, the Option Price in effect immediately prior to such subdivision
shall be proportionately reduced, and the number of Shares then subject to the
Option shall be proportionately increased.  Conversely, if the outstanding
number of Shares of the Company are combined into a smaller number of Shares,
the Option Price in effect immediately prior to such combination shall be
proportionately increased, and the number of Shares then subject to the Option
shall be proportionately reduced.

     8.   Termination of Option.  Unless terminated earlier pursuant to Section
          ---------------------
4 or Section 5(b) hereof, this Option shall terminate upon the first to occur of
the (i) the Expiration Date, or (ii) the date on which Optionee purchases, or in
writing surrenders his right to purchase, all Shares or other securities then
subject to the Option.

     9.   Restriction on Transfer of Option.  The Option may not be sold,
          ---------------------------------
assigned, hypothecated or transferred, except by will or by the laws of descent
and distribution.  Any attempted transfer of the Option in violation of this
provision shall be void and of no effect whatsoever.

     10.  Certain Rights Incident to Divorce.  If an interest in the Option is
          ----------------------------------
required by law to be transferred to a spouse of Optionee pursuant to an order
of a court in a divorce proceeding (notwithstanding the provisions of Section 9
hereof), Optionee shall nevertheless retain all rights with respect to the
exercise of the Option and any interest of such spouse shall be subject to such
rights of Optionee. In addition, if it is determined that Optionee will be
required to pay any taxes attributable to the interest of the spouse in the
Option, any tax liability which is attributable to such spouse's interest shall
be taken into account, and shall reduce such spouse's interest in this Option.

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<PAGE>

     11.  Employment.  Nothing in this Agreement shall confer upon Optionee any
          ----------
right to continue in the employ of the Companies, nor shall this Agreement
interfere in any manner with the right of the Companies to terminate the
employment of Optionee with or without cause at any time.

     12.  Rights as a Shareholder.  Optionee shall have no rights as a
          -----------------------
shareholder of the Company with respect to any Shares covered by the Option
until the exercise of the Option.

     13.  Additional Documents.  The Company and the Optionee will, upon request
          --------------------
of the other party, promptly execute and deliver all additional documents, and
take all such further action, reasonably deemed by such party to be necessary,
appropriate or desirable to complete and evidence the sale, assignment and
transfer of the Shares pursuant to this Agreement.

     14.  Representations, Warranties and Covenants of Optionee.
          -----------------------------------------------------

     (a)  The Optionee acknowledges that the Option has not been registered
under the Securities Act of 1933 or applicable state securities laws on the
grounds that the issuance of the Option is exempt from registration under one or
more provisions of each of such acts. The Optionee further understands that in
determining the availability and applicability of such exemptions and in
executing and delivering this Agreement and issuing and delivering any Shares
upon exercise of the Option, the Company has relied and will rely upon the
representations, warranties and covenants made by the Optionee herein and in any
other documents which he may hereafter deliver to the Company. Accordingly, the
Optionee represents and warrants to and covenants and agrees with the Company
that the Optionee is acquiring and will hold the Option for his own account for
investment and not with a view to any sale or distribution of all or any part
thereof.

     (b)  The Optionee agrees (i) that the certificates representing the Shares
or other securities purchased under this Option may bear such legend or legends
as the Company deems appropriate in order to assure compliance with applicable
securities laws, (ii) that the Company may refuse to register the transfer of
the Shares or other securities purchased under this Option on the transfer
records of the Company unless the Company is provided with an opinion of counsel
in form and substance satisfactory to the Company confirming that such proposed
transfer would not constitute a violation of any applicable securities laws, and
(iii) that the Company may give related instructions to its transfer agent, if
any, to stop registration of the transfer of the Shares or other securities
purchased under this Option.

     (c)  Optionee acknowledges that the value of the Option over its life will
be speculative and uncertain, that there is no market for the Option and it is
unlikely that any market will develop, and consequently, the Optionee may
ultimately realize no value from the Option.

     15.  Notices.  All notices required or permitted to be given hereunder
          -------
shall be in writing and shall be deemed to have been given on the earlier of the
date of receipt by the party to whom the notice is given or five (5) days after
being mailed by certified or registered United States mail, postage prepaid,
addressed to the appropriate party at the address shown beside such party's
signature below or at such other address as such party shall have theretofore
designated by written notice given to the other party.

     16.  Entirety and Modification.  This Agreement contains the entire
          -------------------------
agreement between the parties hereto with respect to the subject matter hereof
and supersedes any and all prior agreements, whether written or oral, between
such parties relating to such subject matter.  No modification, alteration,
amendment or supplement to this Agreement shall be valid or effective unless the
same is in writing and signed by the party against whom it is sought to be
enforced.

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<PAGE>

     17.  Severability.  If any provision of this Agreement is held to be
          ------------
unenforceable, this Agreement shall be considered divisible, and such provision
shall be deemed inoperative to the extent it is unenforceable, and in all other
respects this Agreement shall remain in full force and effect; provided,
however, that if any such provision may be made enforceable by limitation
thereof, then such provision shall be deemed to be so limited and shall be
enforceable to the maximum extent permitted by applicable law.

     18.  Gender.  Words used in this Agreement which refer to Optionee and
          ------
denote the male gender shall also be deemed to include the female gender or the
neuter gender when appropriate.

     19.  Headings.  The headings of the various sections and subsections of
          --------
this Agreement have been inserted for convenient reference only and shall not be
construed to enlarge, diminish or otherwise change the express provisions
hereof.

     20.  Option Subject to Plan.  This Option is subject to the terms and
          ----------------------
conditions of the Plan.  In the event that (i) the Plan is not approved by the
holders of at least a majority of the shares of Common Stock in accordance with
applicable law within twelve months after the date of adoption of the Plan by
the Board or (ii) the transactions contemplated by the Agreement and Plan of
Merger dated as of December 13, 1999, by and among Union Oil Company of
California, the Company, TRH, Inc., and Titan Exploration, Inc. are not
consummated, this Option shall be null and void.

     20.  GOVERNING LAW.  THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN
          -------------
ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE (REGARDLESS OF THE LAWS THAT
MIGHT OTHERWISE GOVERN UNDER APPLICABLE DELAWARE PRINCIPLES OF CONFLICTS OF
LAW).

     21.  Counterparts.  This Agreement may be signed in counterparts, each of
          ------------
which shall be deemed an original and all of which shall constitute one and the
same agreement.

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

                                   PURE RESOURCES, INC.



500 West Texas                By:_____
Suite 200                               Name:_______________________________
Midland, Texas  79701                   Title:______________________________




                                   OPTIONEE



500 West Texas                _____
Suite 200                          Name: [See Schedule 1 attached hereto]
Midland, Texas 79701

                                       6
<PAGE>

                                                                       Exhibit A
                                                                       ---------


                               VESTING SCHEDULE
                                      TO
                      NONQUALIFIED STOCK OPTION AGREEMENT

[*Other than Hightower and Staley:

     The Option shall vest and become exercisable as to one-fourth of the total
Shares which may be purchased hereunder (rounded to the nearest whole share) on
December 13, 2000, shall vest with respect to an additional one-fourth of the
total Shares which may be purchased hereunder (rounded to the nearest whole
share) on December 13, 2001, shall vest with respect to an additional one-fourth
of the total Shares which may be purchased hereunder (rounded to the nearest
whole share) on December 13, 2002, and shall be fully vested on December 13,
2003.]

[*Hightower and Staley:

     The Option shall vest and become exercisable as to one-third of the
total Shares which may be purchased hereunder (rounded to the nearest whole
share) on December 13, 2000, shall vest with respect to an additional one-third
of the total Shares which may be purchased hereunder (rounded to the nearest
whole share) on December 13, 2001, and shall be fully vested on December 13,
2002.]

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<PAGE>

                                  Schedule 1

                                Options Granted


                                     NUmber of Shares
             Name                    Subject to Options
        ---------------------        ------------------

        Jack Hightower                          500,000
        George Staley                           100,000
        Bill White                               40,000
        Jack Rathbone                            50,000
        Gary Dupriest                            75,000
        Tom Moore                                40,000
        Dan Colwell                              40,000
        Rod Woodard                              40,000
        John Benfatti                            35,000
        Susan Rowland                            35,000
        Darin Holderness                         35,000

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