Document:

<PAGE>   1
                                                                   Exhibit 10.15

                                 GRAFTECH INC.
                         EMPLOYEE EQUITY INCENTIVE PLAN

                      NONQUALIFIED STOCK OPTION AGREEMENT

            NONQUALIFIED STOCK OPTION AGREEMENT (this "Option Agreement")
between Graftech Inc. (the "Corporation") and       (the "Participant"), dated
as of the effective date of the registration statement filed by the Corporation
with the Securities and Exchange Commission in connection with the initial
public offering of shares of common stock of the Corporation (the "Grant Date").
Notwithstanding anything contained herein to the contrary, this Option Agreement
shall become null and void if such effective date does not occur before
September 30, 2000 or the closing of such offering does not occur within 30 days
after such effective date.

                                   BACKGROUND

            The Board of Directors of the Corporation has determined that it
would be in the best interests of the Corporation and its stockholders to adopt,
and accordingly has adopted, the Graftech Inc. Employee Equity Incentive Plan
(the "Plan"), a copy of which has been furnished to the Participant, to provide
incentives to certain employees of the Corporation and its subsidiaries by
providing them with opportunities to purchase shares of common stock of the
Corporation. Pursuant thereto, the options provided herein have been granted to
the Participant.

            In consideration of the agreements contained herein and other good
and valuable consideration, receipt of which is hereby acknowledged, the parties
agree as follows:

                                    ARTICLE I

                                DEFINITIONS; PLAN

            Unless otherwise indicated, whenever capitalized terms are used in
this Option Agreement, they shall have the meanings set forth in the Plan as in
effect on the Grant Date (but as amended thereafter to the extent such
amendments are applicable hereto pursuant to the terms thereof). The Plan as in
effect on the Grant Date (but as amended thereafter to the extent such
amendments are applicable hereto pursuant to the terms thereof) is hereby
incorporated by reference.

                                   ARTICLE II

                                GRANT OF OPTIONS

      2.1 Grant of Options. The Participant is hereby granted Options
representing the right to purchase ________ shares of Common Stock on the terms
and subject to the conditions specified herein. Such Options are Nonqualified
Stock Options and are not intended to constitute Incentive Stock Options. Unless
otherwise indicated herein, references herein to
<PAGE>   2
"Options" mean the Options granted hereby and referenced herein to "Option
Shares" mean the shares of Common Stock which may be purchased upon exercise of
Options.

      2.2 Exercise Price. The Exercise Price of the Options is $ ______ per
share (i.e., the Fair Market Value of the Common Stock on the Grant Date).

                                  ARTICLE III

                            EXERCISABILITY OF OPTIONS

            Options shall vest upon the earliest to occur of the events
described in Sections 3.1, 3.2 or 3.3, but subject to the limitations set forth
in Section 3.5, and shall become exercisable as described in Section 3.4:

      3.1 Vesting upon Change in Control. If not sooner vested, all Options
shall vest upon the occurrence of a Change in Control of the Corporation.

      3.2 Time Vesting. Options as to the first one-third (_____) of the Option
Shares shall vest on the third anniversary of the Grant Date; Options as to the
second one-third (____) of the Options Shares shall vest on the fourth
anniversary of the Grant Date; and Options as to the last one-third (_____) of
the Option Shares shall vest on the fifth anniversary of the Grant Date.

      3.3 Discretionary Vesting. The Committee or the Board may, in its sole
discretion, accelerate the vesting of any or all Options at any time and for any
reason so long as the prior written consent of UCAR shall have been obtained if
so required by the Plan.

      3.4 Exerciseability. Options shall become exercisable as to the Option
Shares as to which they are vested at the time they first vest and shall cease
to be exercisable at the time they expire as provided in Article V.

      3.5 Effect of Termination of Employment on Vesting and Exercisability.
Unless otherwise determined by the Board or the Committee, unvested Options
shall cease to vest, shall cease to be exercisable and shall expire upon the
first to occur of: (i) the Participant's Retirement, death or Disability; (ii)
the Participant's termination of employment by the Corporation or its
Subsidiaries (together with the Corporation, the "Company") without Cause or
upon lay-off; (iii) the Participant's termination of employment for Cause; (iv)
the Participant's resignation from employment; or (v) expiration of the Options
as provided in Article V.

                                   ARTICLE IV

                               EXERCISE OF OPTIONS

      4.1 Person Who Can Exercise. Options may only be exercised by the
Participant or a Permitted Transferee, except that, in the event of his
Disability, Options may be exercised by his legal guardian or legal
representative and, in the event of his death, Options may be exercised by the
executor or administrator of his estate or the person to whom his rights under
the Options pass by will or the laws of descent and distribution.

                                       2
<PAGE>   3
      4.2 Procedure for Exercise. Vested Options may be exercised in whole or in
part with respect to any portion thereof that is exercisable. To exercise an
Option, the Participant (or such other person who shall be permitted to exercise
the Option as set forth in Section 4.1) must complete, sign and deliver to the
Corporation a written notice of exercise (in the form provided by the
Corporation) together with payment in full of the Exercise Price multiplied by
the number of Option Shares with respect to which the Option is exercised.
Payment of the Exercise Price shall be made in: (i) cash (including check, bank
draft or money order); (ii) whole shares of Common Stock; or (iii) combination
of cash and whole shares of Common Stock. The value of any share of Common Stock
delivered in payment of the Exercise Price shall be its Fair Market Value on the
date the Option is exercised. The Option shall be deemed exercised only upon
satisfaction of all conditions set forth herein and in the written notice of
exercise.

            In lieu of paying the Exercise Price, upon the Participant's (or
such other person's) request, with the Committee's or the Board's consent (which
may or may not be given in its sole discretion), the Corporation shall deliver
to the Participant upon such exercise a number of shares of Common Stock equal
to (A) divided by (B) where (A) is the excess of (i) the Fair Market Value of a
share of Common Stock, over (ii) the Exercise Price, multiplied by (iii) the
number of shares for which the Option is being exercised, and (B) the Fair
Market Value of a share of Common Stock.

      4.3 Conditional Exercise in Contemplation of Accelerated Vesting. In
contemplation of an Acceleration Event, the Participant (or such other person
who shall be permitted to exercise Options as set forth in Section 4.1) may
conditionally exercise, at least 30 days prior to such Acceleration Event, all
or a portion of the Options which are exercisable and which will become
exercisable upon such Acceleration Event. Such conditional exercise shall become
null and void if such Acceleration Event does not occur within six (6) months
following the date of such conditional exercise. A conditional exercise shall
become binding upon the Participant (or such other person) and such Participant
(or such other person) shall become obligated to pay the Exercise Price therefor
upon the occurrence of such Acceleration Event.

      4.4 Limited Stock Appreciation Right. Upon the request of the Participant
(or such other Person who shall be permitted to exercise Options as set forth in
Section 4.1), the Corporation may, in its sole discretion, cancel any Option (in
whole or in part) and pay the Participant the excess of the (i) the Fair Market
Value of a share of Common Stock, over (ii) the Exercise Price, multiplied by
(iii) the number of Option Shares subject to the Option which is being cancelled
(the "Cancellation Amount"); provided, however, that, coincident with any
transaction which is reasonably likely to result in a Change in Control of the
Corporation, the Corporation may, in its sole discretion, without the
Participant's consent, cancel any Option (in whole or in part) and pay the
Participant the Cancellation Amount.

      4.5 Withholding of Taxes. The Company shall withhold from any amounts due
and payable by the Company to the Participant (or secure payment from the
Participant in lieu of withholding) the amount of any withholding or other tax
due from the Corporation with respect to any Option Shares issuable under this
Option Agreement, and the Corporation may defer such issuance until such
withholding or payment is made unless otherwise indemnified to its satisfaction
with respect thereto. The Corporation shall have the right to: (i) make
deductions from any settlement of Options, including the delivery or vesting of
Option Shares, or require

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<PAGE>   4
Option Shares or cash, or both, be withheld from any settlement of Options, in
each case in an amount sufficient to satisfy the withholding or other tax
obligation; or (ii) take such other action as may be necessary or appropriate to
satisfy the withholding or other tax obligation.

                                   ARTICLE V

                              EXPIRATION OF OPTIONS

      5.1 Expiration. Options shall expire at 5:00 p.m., Eastern Standard or
Daylight Savings Time (whichever is then in effect), on the tenth anniversary of
the Grant Date.

      5.2 Earlier Expiration. Notwithstanding Section 5.1, Options shall expire
as provided in Section 3.5 and shall also expire as follows:

            (a) Upon the Participant's termination of employment for Cause, all
vested Options shall expire immediately; and

            (b) Upon the Participant's termination of employment by the Company
without Cause or upon lay-off or the Participant's resignation from employment,
all vested Options shall expire upon the earlier of: (i) the third anniversary
of such termination, lay-off, or resignation; or (ii) the expiration of Options
under Section 5.1.

                                   ARTICLE VI

                                  MISCELLANEOUS

      6.1 Options Not Transferable. Options may not be transferred (which
includes, pledge, assign, hypothecate or other disposition) by the Participant,
except: (i) by will or laws of descent and distribution; (ii) pursuant to a
Qualified Domestics Relation Order (as defined in Section 414(p) of the Code);
or (iii) to a Permitted Transferee. Any attempt to effect a transfer of Options
that is not otherwise permitted by the Board, the Committee, the Plan or this
Option Agreement shall be null and void.

      6.2 Noncompete and Confidentiality Covenants. If the Participant breaches
any confidentiality or noncompete covenant that the Participant has entered into
with the Company, then, notwithstanding the terms of this Option Agreement, the
Participant: (i) shall immediately forfeit the right to exercise all vested and
unvested Options outstanding after the date of the first such violation; and
(ii) will be obligated to pay the Corporation, as liquidated damages, an amount
equal to the gross amount of all gains realized upon the exercise of all Options
at any time after the date of the first such violation. The Board or the
Committee may, in its discretion, waive this Section 6.2.

      6.3 Adjustments. Upon the occurrence of any stock split or reverse stock
split, stock dividend, stock exchange, recapitalization, merger, consolidation,
business combination or other major corporate change, or in the event of any
special distribution to stockholders, the number and/or kind of Option Shares
and/or the Exercise Price shall be adjusted in accordance with the provisions of
the Plan.

                                       4
<PAGE>   5
      6.4 Notices. All notices, requests and demands to or upon a party must, to
be effective, be given in writing and shall be deemed to have been duly given
when delivered by hand or three days after deposited in the mail, postage
prepaid, or, in the case of facsimile notice, when received, addressed as
follows or to such other address of which the transmitting party shall have been
duly notified hereunder:

            (a) If to the Corporation, to the following address:

                Graftech Inc.
                ______________________________
                ______________________________
                Attn: ________________________
                Facsimile:____________________

            (b) If to the Participant, to the address or facsimile number as
shown on the signature page hereto.

      6.5 No Right as Stockholder. The Participant shall not have any rights or
privileges of a stockholder of the Corporation with respect to any Option Shares
subject to (but not acquired upon valid exercise of) Options, nor shall the
Corporation have any obligation to pay any dividends or distributions, give any
stockholder notices or afford any other rights to which a holder of shares of
Common Stock is entitled to the Participant with respect to Option Shares, until
the due exercise of the Options relating to such Option Shares.

      6.6 No Right to Continued Employment. Nothing in this Option Agreement
shall confer upon the Participant any right to continue as an employee of the
Company or interfere in any way with the right of the Company to terminate the
Participant's employment at any time.

      6.7 Amendment. Except as otherwise provided in the Plan, this Option
Agreement may be amended only by a writing executed by the parties which
specifically states that it is amending this Option Agreement.

      6.8 Governing Law. Without limiting the provisions of the Plan,
jurisdiction over disputes with regard to the validity, construction and effect
of this Option Agreement, and all actions taken or relating to the Option
Agreement, shall be vested exclusively in the courts of the State of Delaware,
and this Option Agreement shall be construed and interpreted in accordance with
and governed by the laws of the State of Delaware, other than the conflict of
laws provisions of such laws.

      6.9 Construction. Without limiting the provisions of the Plan, the
construction of this Option Agreement is vested in the Board or the Committee,
and the Board's or the Committee's construction shall be final and conclusive on
all persons.

      6.10 Titles. Titles are provided herein for convenience only and are not
to serve as a basis for interpretation or construction of this Option Agreement.

                                       5
<PAGE>   6
            IN WITNESS WHEREOF, this Option Agreement has been executed and
delivered by the parties.

PARTICIPANT                               GRAFTECH INC.

--------------------------------------    --------------------------------------
Name:                                     Name:

                                          --------------------------------------
                                          Title:

--------------------------------------
Address:

--------------------------------------
Phone:

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Facsimile:

                                       6<PAGE>   1
                                                                   Exhibit 10.16

                                  GRAFTECH INC.
                     OUTSIDE DIRECTOR EQUITY INCENTIVE PLAN

                       NONQUALIFIED STOCK OPTION AGREEMENT

            NONQUALIFIED STOCK OPTION AGREEMENT (this "Option Agreement")
between Graftech Inc. (the "Corporation") and           (the "Participant"),
dated as of the effective date of the registration statement filed by the
Corporation with the Securities and Exchange Commission in connection with the
initial public offering of shares of common stock of the Corporation (the "Grant
Date"). Notwithstanding anything contained herein to the contrary, this Option
Agreement shall become null and void if such effective date does not occur
before September 30, 2000 or the closing of such offering does not occur within
30 days after such effective date.

                                   BACKGROUND

            The Board of Directors of the Corporation has determined that it
would be in the best interests of the Corporation and its stockholders to adopt,
and accordingly has adopted, the Graftech Inc. Outside Director Equity Incentive
Plan (the "Plan"), a copy of which has been furnished to the Participant, to
provide incentives to outside directors of the Corporation by providing them
with opportunities to purchase shares of common stock of the Corporation.
Pursuant thereto, the options provided herein have been granted to the
Participant.

            In consideration of the agreements contained herein and other good
and valuable consideration, receipt of which is hereby acknowledged, the parties
agree as follows:

                                   ARTICLE I

                                DEFINITIONS; PLAN

            Unless otherwise indicated, whenever capitalized terms are used in
this Option Agreement, they shall have the meanings set forth in the Plan as in
effect on the Grant Date (but as amended thereafter to the extent such
amendments are applicable hereto pursuant to the terms thereof). The Plan as in
effect on the Grant Date (but as amended thereafter to the extent such
amendments are applicable hereto pursuant to the terms thereof) is hereby
incorporated by reference.

                                   ARTICLE II

                                GRANT OF OPTIONS

2.1 Grant of Options. The Participant is hereby granted Options representing the
right to purchase ________ shares of Common Stock on the terms and subject to
the conditions specified herein. Unless otherwise indicated herein, references
herein to "Options" mean the Options granted hereby and referenced herein to
"Option Shares" mean the shares of Common Stock which may be purchased upon
exercise of Options.
<PAGE>   2
2.2 Exercise Price. The Exercise Price of the Options is $ ______ per share
(i.e., the Fair Market Value of the Common Stock on the Grant Date).

                                  ARTICLE III

                            EXERCISABILITY OF OPTIONS

            Options shall vest upon the earliest to occur of the events
described in Sections 3.1, 3.2 or 3.3, but subject to the limitations set forth
in Section 3.5, and shall become exercisable as described in Section 3.4:

      3.1 Vesting upon Change in Control. If not sooner vested, all Options
shall vest upon the occurrence of a Change in Control of the Corporation.

      3.2 Time Vesting. Options as to all of the Option Shares shall vest on the
earlier of: (i) the third anniversary of the Grant Date; or (ii) immediately
after UCAR ceases to own or hold, directly or indirectly, a majority of the then
outstanding shares of Common Stock, but in any event not earlier than the first
anniversary of the Grant Date.

      3.3 Discretionary Vesting. The Committee or the Board may, in its sole
discretion, accelerate the vesting of any or all Options at any time and for any
reason so long as the prior written consent of UCAR shall have been obtained (if
so required by the Plan).

      3.4 Exerciseability. Options shall become exercisable as to the Option
Shares as to which they are vested at the time they first vest and shall cease
to be exercisable at the time they expire as provided in Article V.

      3.5 Effect of Termination as a Director on Vesting and Exercisability.
Unless otherwise determined by the Board or the Committee, unvested Options
shall cease to vest, shall cease to be exercisable and shall expire upon the
first to occur of: (i) the Participant ceasing to be a director of the
Corporation for any reason; or (ii) expiration of the Options as provided in
Article V.

                                   ARTICLE IV

                               EXERCISE OF OPTIONS

      4.1 Person Who Can Exercise. Options may only be exercised by the
Participant or a Permitted Transferee, except that, in the event of his
Disability, Options may be exercised by his legal guardian or legal
representative and, in the event of his death, Options may be exercised by the
executor or administrator of his estate or the person to whom his rights under
the Options pass by will or the laws of descent and distribution.

      4.2 Procedure for Exercise. Vested Options may be exercised in whole or in
part with respect to any portion thereof that is exercisable. To exercise an
Option, the Participant (or such other person who shall be permitted to exercise
the Option as set forth in Section 4.1) must complete, sign and deliver to the
Corporation a written notice of exercise (in the form provided by the
Corporation) together with payment in full of the Exercise Price multiplied by
the number

                                       2
<PAGE>   3
of Option Shares with respect to which the Option is exercised. Payment of the
Exercise Price shall be made in: (i) cash (including check, bank draft or money
order); (ii) whole shares of Common Stock; or (iii) combination of cash and
whole shares of Common Stock. The value of any share of Common Stock delivered
in payment of the Exercise Price shall be its Fair Market Value on the date the
Option is exercised. The Option shall be deemed exercised only upon satisfaction
of all conditions set forth herein and in the written notice of exercise.

            In lieu of paying the Exercise Price, upon the Participant's (or
such other person's) request, with the Committee's or the Board's consent (which
may or may not be given in its sole discretion), the Corporation shall deliver
to the Participant upon such exercise a number of shares of Common Stock equal
to (A) divided by (B) where (A) is the excess of (i) the Fair Market Value of a
share of Common Stock, over (ii) the Exercise Price, multiplied by (iii) the
number of shares for which the Option is being exercised, and (B) the Fair
Market Value of a share of Common Stock.

      4.3 Conditional Exercise in Contemplation of Accelerated Vesting. In
contemplation of an Acceleration Event, the Participant (or such other person
who shall be permitted to exercise Options as set forth in Section 4.1) may
conditionally exercise, at least 30 days prior to such Acceleration Event, all
or a portion of the Options which are exercisable and which will become
exercisable upon such Acceleration Event. Such conditional exercise shall become
null and void if such Acceleration Event does not occur within six (6) months
following the date of such conditional exercise. A conditional exercise shall
become binding upon the Participant (or such other person) and such Participant
(or such other person) shall become obligated to pay the Exercise Price therefor
upon the occurrence of such Acceleration Event.

      4.4 Limited Stock Appreciation Right. Upon the request of the Participant
(or such other Person who shall be permitted to exercise Options as set forth in
Section 4.1), the Corporation may, in its sole discretion, cancel any Option (in
whole or in part) and pay the Participant the excess of the (i) the Fair Market
Value of a share of Common Stock, over (ii) the Exercise Price, multiplied by
(iii) the number of Option Shares subject to the Option which is being cancelled
(the "Cancellation Amount"); provided, however, that, coincident with any
transaction which is reasonably likely to result in a Change in Control of the
Corporation, the Corporation may, in its sole discretion, without the
Participant's consent, cancel any Option (in whole or in part) and pay the
Participant the Cancellation Amount.

                                   ARTICLE V

                              EXPIRATION OF OPTIONS

      5.1 Expiration. Options shall expire at 5:00 p.m., Eastern Standard or
Daylight Savings Time (whichever is then in effect), on the tenth anniversary of
the Grant Date.

      5.2 Earlier Expiration. Notwithstanding Section 5.1, Options shall expire
as provided in Section 3.5 and shall also expire four years following the date
on which the Participant ceases to be a director for any reason.

                                       3
<PAGE>   4
                                   ARTICLE VI

                                  MISCELLANEOUS

      6.1 Options Not Transferable. Options may not be transferred (which
includes pledge, assign, hypothecate or other disposition) by the Participant,
except: (i) by will or laws of descent and distribution; (ii) pursuant to a
Qualified Domestics Relation Order (as defined in Section 414(p) of the Code);
or (iii) to a Permitted Transferee. Any attempt to effect a transfer of Options
that is not otherwise permitted by the Board, the Committee, the Plan or this
Option Agreement shall be null and void.

      6.2 Adjustments. Upon the occurrence of any stock split or reverse stock
split, stock dividend, stock exchange, recapitalization, merger, consolidation,
business combination or other major corporate change, or in the event of any
special distribution to stockholders, the number and/or kind of Option Shares
and/or the Exercise Price shall be adjusted in accordance with the provisions of
the Plan.

      6.3 Notices. All notices, requests and demands to or upon a party must, to
be effective, be given in writing and shall be deemed to have been duly given
when delivered by hand or three days after deposited in the mail, postage
prepaid, or, in the case of facsimile notice, when received, addressed as
follows or to such other address of which the transmitting party shall have been
duly notified hereunder:

            (a) If to the Corporation, to the following address:

                  Graftech Inc.

                  Attn:
                  Facsimile:

            (b) If to the Participant, to the address or facsimile number as
shown on the signature page hereto.

      6.4 No Right as Stockholder. The Participant shall not have any rights or
privileges of a stockholder of the Corporation with respect to any Option Shares
subject to (but not acquired upon valid exercise of) Options, nor shall the
Corporation have any obligation to pay any dividends or distributions, give any
stockholder notices or afford any other rights to which a holder of shares of
Common Stock is entitled to the Participant with respect to Option Shares, until
the due exercise of the Options relating to such Option Shares.

      6.5 No Right to Continued Service. Nothing in this Option Agreement shall
confer upon the Participant the right to continue service as a member of the
Board or to be entitled to any remuneration or benefits not set forth in the
Plan or this Option Agreement.

      6.6 Amendment. Except as otherwise provided in the Plan, this Option
Agreement may be amended only by a writing executed by the parties which
specifically states that it is amending this Option Agreement.

                                       4
<PAGE>   5
      6.7 Governing Law. Without limiting the provisions of the Plan,
jurisdiction over disputes with regard to the validity, construction and effect
of this Option Agreement, and all actions taken or relating to the Option
Agreement, shall be vested exclusively in the courts of the State of Delaware,
and this Option Agreement shall be construed and interpreted in accordance with
and governed by the laws of the State of Delaware, other than the conflict of
laws provisions of such laws.

      6.8 Construction. Without limiting the provisions of the Plan, the
construction of this Option Agreement is vested in the Board or the Committee,
and the Board's or the Committee's construction shall be final and conclusive on
all persons.

      6.9 Titles. Titles are provided herein for convenience only and are not to
serve as a basis for interpretation or construction of this Option Agreement.

            IN WITNESS WHEREOF, this Option Agreement has been executed and
delivered by the parties.

<TABLE>
<CAPTION>
<S>                                     <C>
PARTICIPANT                             GRAFTECH INC.

----------------------------------      --------------------------------------
Name:                                   Name:

                                        --------------------------------------
                                        Title:
----------------------------------
Address:

----------------------------------
Phone:

----------------------------------
Facsimile:
</TABLE>

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