Exhibit 4.1 [ ] CLASS A WARRANTS, EACH WARRANT ENTITLING THE HOLDER TO PURCHASE ONE COMMON SHARE OF ARCH CAPITAL GROUP LTD. ARCH CAPITAL GROUP LTD. THIS WARRANT (THE "WARRANT") AND THE UNDERLYING COMMON SHARES MAY NOT BE TRANSFERRED, OFFERED OR SOLD EXCEPT (A) IN COMPLIANCE WITH THE PROVISIONS OF A CERTAIN SUBSCRIPTION AGREEMENT AND A CERTAIN SHAREHOLDERS AGREEMENT EXECUTED IN CONNECTION HEREWITH AND (B) PURSUANT TO (1) AN EFFECTIVE REGISTRATION STATEMENT UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED, OR (2) AN APPLICABLE EXEMPTION FROM REGISTRATION THEREUNDER. ANY SALE PURSUANT TO CLAUSE (B)(2) OF THE PRECEDING SENTENCE MUST BE ACCOMPANIED BY AN OPINION OF WACHTELL, LIPTON, ROSEN & KATZ, OR SUCH OTHER COUNSEL AS IS REASONABLY SATISFACTORY TO ARCH CAPITAL GROUP LTD., TO THE EFFECT THAT SUCH EXEMPTION FROM REGISTRATION IS AVAILABLE IN CONNECTION WITH SUCH SALE. ARCH CAPITAL GROUP LTD., a Bermuda exempted limited company (the "Company"), hereby certifies that, for value received, [ ] (the "Holder"), or its assigns, is entitled, subject to the terms set forth below, to purchase from the Company, at any time and from time to time in whole or in part, an aggregate of [ ] fully paid and nonassessable common shares, par value $.01 per share ("Common Shares"), of the Company during the period beginning on the date of issuance hereof (the "Closing Date") and ending on September 19, 2002 (the "Exercise Period"). 1. PURCHASE PRICE. Such Common Shares shall be purchased at a purchase price per share, subject to the provisions of Paragraph 3 hereof, equal to $20.00 (as adjusted in accordance with the terms hereof, the "Purchase Price"). The number and character of such Common Shares are subject to adjustment as provided below, and the term "Common Shares" shall mean, unless the context otherwise requires, the Common Shares or other securities or property at the time deliverable upon the exercise of this Warrant. -2- 2. EXERCISE OF WARRANT. The purchase rights evidenced by this Warrant shall be exercised by the Holder surrendering this Warrant, with the form of subscription at the end hereof duly executed by such Holder (the "Exercise Notice"), to the Company at its offices, 20 Horseneck Lane, Greenwich, Connecticut 06830, accompanied by payment as specified below of the aggregate Purchase Price determined as of the Determination Date (as defined below) of the Common Shares being purchased pursuant to such exercise. Payment of the aggregate Purchase Price may be made, at the option of the Holder, (i) in cash, (ii) by certified check or bank cashier's check payable to the order of the Company in the amount of such Purchase Price, (iii) by delivering Common Shares with an aggregate Market Price (as hereinafter defined) as of the day prior to the Company's receipt of the Exercise Notice (the "Determination Date") equal to the product of the Purchase Price and the number of Common Shares being purchased, (iv) by the Company reducing, at the request of the Holder, the number of Common Shares for which this Warrant is exercisable by a number of Common Shares (the "Surrendered Stock") such that the product of (a) the Market Price per Common Share as of the Determination Date less the Purchase Price in effect on the Determination Date multiplied by (b) the Surrendered Stock equals or exceeds the product of (x) the Purchase Price in effect on the Determination Date and (y) the number of Common Shares being purchased, or any combination of the methods of payment described in clauses (i) through (iv) above. 2.1. Partial Exercise. This Warrant may be exercised for less than the full number of Common Shares at the times called for hereby, in which case the number of Common Shares receivable upon the exercise of this Warrant as a whole, the sum payable upon the exercise of this Warrant as a whole, shall be proportionately reduced. Upon any such partial exercise, the Company at its expense will forthwith issue to the Holder hereof a new Warrant or Warrants of like tenor for the number of Common Shares as to which rights have not been exercised, such Warrant or Warrants to be issued in the name of the Holder hereof or his nominee (upon payment by such Holder of any applicable transfer taxes). 2.2. Delivery of Certificates for Common Shares on Conversion. As soon as practicable after the exercise of this Warrant and payment of the Purchase Price, and in any event within ten (10) days thereafter, the Company, at its expense, will cause to be issued in the name of and delivered to the Holder hereof a certificate or certificates for the number of fully paid and nonassessable Common Shares or other securities or property to which such Holder shall be entitled upon such exercise, plus, in lieu of any fractional share to which such Holder would otherwise be entitled, cash in an amount determined in accordance with Paragraph 3.9 hereof. The Company agrees that the Common Shares so received shall be deemed to be issued to the Holder as the record owner of such Common Shares as of the close of business on the date on which this Warrant shall have been surrendered and payment for such Common Shares made as aforesaid. 3. ANTI-DILUTION PROVISIONS AND OTHER ADJUSTMENTS. In order to prevent dilution of the right granted hereunder, the Purchase Price shall be subject to adjustment from time to time in accordance with this Paragraph 3. Upon each adjustment of the Purchase Price pursuant to this Paragraph 3, the registered holder hereof shall thereafter be entitled to acquire upon exercise of this Warrant, at the Purchase Price resulting from such adjustment, the number of shares of the Company's Common Shares obtainable by multiplying the Purchase Price in effect immediately prior to such adjustment by the number of shares of the Company's Common Shares acquirable upon -3- conversion thereof immediately prior to such adjustment and dividing the product thereof by the Purchase Price resulting from such adjustment. 3.1. Adjustment for Issue or Sale of Common Shares. Except as provided in Paragraph 3.5 below, if and whenever on or after the date of issuance hereof the Company shall issue or sell, or shall in accordance with subparagraphs (1) to (8) of this Paragraph 3.1 inclusive, be deemed to have issued or sold any Common Shares to any person for a consideration per share less than the Market Price (or, in the case of an issuance or sale in connection with an underwritten public offering, 99% of the Market Price less underwriting discounts and commissions) in effect immediately prior to the time of such issue or sale, then forthwith upon such issue or sale (each, a "Triggering Transaction"), the Purchase Price shall, subject to subparagraphs (1) to (8) of this Paragraph 3.1, be reduced to the Purchase Price (calculated to the nearest tenth of a cent) determined by multiplying the Purchase Price in effect immediately prior to the time of such Triggering Transaction by a fraction, the numerator of which shall be the sum of (x) the product of the Number of Common Shares Deemed Outstanding (as defined below) immediately prior to such Triggering Transaction multiplied by the Market Price immediately prior to such Triggering Transaction plus (y) the total amount, if any, received or receivable at any time by the Company as consideration for the issuance or sale of such Common Shares, and the denominator of which shall be the product of (x) the Number of Common Shares Deemed Outstanding immediately after such Triggering Transaction, multiplied by (y) the Market Price immediately prior to such Triggering Transaction; provided that in the case of a sale of Common Shares pursuant to a purchase, underwriting or similar agreement, the Market Price shall mean the Market Price in effect upon the date such agreement is executed by the Company. For purposes of this Paragraph 3, the term "Number of Common Shares Deemed Outstanding" at any given time shall mean the sum of (i) the number of Common Shares outstanding at such time, and (ii) the number of Common Shares deemed to be outstanding under subparagraphs (1) to (8) of this Paragraph 3, inclusive, at such time. For purposes of this Paragraph 3, inclusive, at such time. For purposes of this Paragraph 3, the term "Market Price" shall mean, as of any date, (a) for any period during which a security shall be listed for trading on a national securities exchange or on the Nasdaq Stock Market ("Nasdaq"), or (in the case of non-United States securities) similar securities exchange, the closing price per share of such security as of such day, or, in case no reported sale occurs on such trading day, the mean of the reported closing bid and asked prices per share for the prior five trading days ending on such day, (b) for any period during which such security shall not be so listed, but when prices for such security shall be reported by Nasdaq or similar system in the case of non-U.S. securities, the mean of the most recent average bid and asked prices per share as quoted by Nasdaq or such other system or (c) the market price per share of such security as determined by the Board of Directors of the Company (the "Board of Directors") as of the next preceding day, in the event neither (a) nor (b) above shall be applicable, or in the event the Board of Directors shall be in good faith determine that application of (a) or (b) would not result in a fair determination of the Market Price. For purposes of determining the adjusted Purchase Price under this Paragraph 3.1, the following subparagraphs (1) to (8), inclusive, shall be applicable: -4- (1) In case the Company at any time shall in any manner issue or sell (whether directly or by assumption in a merger or otherwise) any rights to subscribe for or to purchase, or any options for the purchase of, Common Shares or any other securities convertible into or exchangeable or exercisable for Common Shares (such rights or options being herein called "Options" and such convertible, exchangeable or exercisable shares or securities being herein called "Convertible Securities"), whether or not such Options or the right to convert, exercise or exchange any such Convertible Securities are immediately exercisable, and the price per share for which Common Shares are issuable upon exercise, conversion or exchange (determined by dividing (x) the total amount, if any, received or receivable by the Company as consideration for the issuing of such Options, plus the minimum aggregate amount of additional consideration payable to the Company upon the exercise of all such Options, by (y) the total maximum number of Common Shares issuable upon the exercise of such Options or the conversion or exchange of such Convertible Securities) shall be less than the Market Price (or, in the case of an issuance or sale in connection with an underwritten public offering, less than 99% of the Market Price less underwriting discounts and commissions), determined as of the date of such issuance or sale (or, in the case of an issuance or sale pursuant to a purchase, underwriting or similar agreement, the Market Price determined as of the date such agreement is executed by the Company), then the total maximum number of Common Shares issuable upon exercise of such Options or conversion or exchange of all such Convertible Securities shall (as of the date of the grant of such Option) be deemed to be outstanding and to have been issued and sold by the Company for such price per share. No adjustment of the Purchase Price shall be made upon exercise of such Options or conversion or exchange of such Convertible Securities, except as otherwise provided in subparagraph (3) below. (2) In case the Company at any time shall in any manner issue or sell (whether directly or by assumption in a merger or otherwise) any Convertible Securities, whether or not the rights to exchange, exercise or convert thereunder are immediately exercisable, and the price per share for which Common Shares are issuable upon such conversion, exercise or exchange (determined by dividing (x) the total amount received or receivable by the Company as consideration for the issue or sale of such Convertible Securities, plus the minimum aggregate amount of additional consideration, if any, payable to the Company upon the conversion or exchange thereof, by (y) the total maximum number of Common Shares issuable upon the conversion or exchange of all such Convertible Securities) shall be less than the Market Price (or, in the case of an issuance or sale in connection with an underwritten public offering, less than 99% of the Market Price less underwriting discounts and commissions), determined as of the date of such issuance or sale (or, in the case of an issuance or sale pursuant to a purchase, underwriting or similar agreement, the Market Price determined as of the date such agreement is executed by the Company), then the total maximum number of Common Shares issuable upon conversion or exchange of all such Convertible Securities shall (as of the date of the issue or sale of such Convertible Securities) be deemed to be outstanding and to have been issue and sold by the Company for such price per share. No adjustment of the Purchase Price shall be made upon the actual issue of such Common Shares upon exercise of the rights to exchange or convert under such Convertible Securities, except as otherwise provided in subparagraph (3) below. -5- (3) If the exercise price provided for in any Options referred to in subparagraph (1), the additional consideration, if any, payable upon the conversion or exchange of any Convertible Securities referred to in subparagraph (1) or (2), or the rate at which any Convertible Securities referred to in subparagraph (1) or (2) are convertible into or exchangeable for Common Shares, shall change at any time (other than under or by reason of provisions designed to protect against dilution of the type set forth in Paragraph 3.1 or 3.3), the Purchase Price in effect at the time of such change shall forthwith be readjusted to the Purchase Price which would have been in effect at the time had such Options or Convertible Securities still outstanding provided for such changed purchase price, additional consideration or conversion or exchange rate, as the case may be, at the time initially granted, issued or sold. If the exercise price provided for in any Option referred to in subparagraph (1), the additional consideration, if any, payable upon the conversion or exchange of any Convertible Securities referred to in subparagraph (1) or (2), or the rate at which any Convertible Securities referred to in subparagraph (1) or (2) are convertible into or exchangeable for Common Shares, shall be reduced at any time under or by reason of provisions with respect thereto designed to protect against dilution, then the Purchase Price then in effect hereunder shall forthwith be adjusted to such respective amount as would have been obtained had such Option or Convertible Security never been issued as to such Common Shares and had adjustments been made upon the issuance of Common Shares delivered as aforesaid, but only if as a result of such adjustment the Purchase Price then in effect hereunder is hereby reduced and provided that there shall be no duplication of any adjustments otherwise made in accordance with the terms hereof. (4) On the expiration of any Option or the termination of any right to convert or exchange any Convertible Securities, the Purchase Price then in effect hereunder shall forthwith be increased to the Purchase Price which would have been in effect at the time of such expiration or termination had such Option or Convertible Securities, to the extent outstanding immediately prior to such expiration or termination, never been issued. (5) In case any Options shall be issued in connection with the issue or sale of other securities of the Company, together comprising one integral transaction in which no specific consideration is allocated to such Options by the parties thereto, such Options shall be deemed to have been issued without consideration. (6) In case any Common Shares, Options or Convertible Securities shall be issued or sold or deemed to have been issued or sold for cash, the consideration received therefor shall be deemed to be the amount received by the Company therefor. In case any Common Shares, Options or Convertible Securities shall be issued or sold for a consideration other than cash, the amount of the consideration other than cash received by the Company shall be the fair value of such consideration as determined in good faith by the Board of Directors. (7) The number of Common Shares outstanding at any given time shall not include shares owned or held by or for the account of the Company, but the disposition of any -6- shares so owned or held shall be considered an issue or sale of Common Shares for the purpose of this Paragraph 3.1. (8) In case the Company shall declare a dividend or make any other distribution upon the stock of the Company payable in Common Shares, Options or Convertible Securities, then in such case any Common Shares, Options or Convertible Securities, as the case may be, issuable in payment of such dividend or distribution shall be deemed to have been issued or sold without consideration. 3.2. Determination of Date of Issuance or Sale of Common Shares. For purposes of Paragraph 3.1, in case the Company shall take a record of the holders of its Common Shares for the purpose of determining holders entitled (x) to receive a dividend or other distribution payable in Common Shares, Options or Convertible Securities, or (y) to subscribe for or purchase Common Shares, Options or Convertible Securities, then such record date shall be deemed to have been issued or sold upon the declaration of such dividend or the making of such other distribution or the date of the granting of such right or subscription or purchase, as the case may be. 3.3. Subdivisions and Combinations. In case the Company shall at any time subdivide (other than by means of a dividend payable in Common Shares covered by subparagraph 3.1(8)) its outstanding Common Shares into a greater number of shares, the Purchase Price in effect immediately prior to such subdivision shall be appropriately reduced, and, conversely, in case the outstanding Common Shares of the Company shall be combined into a smaller number of shares, the Purchase Price in effect immediately prior to such combination shall be proportionately increased. 3.4. Reorganization, Reclassification, Consolidation, Merger or Sale of Assets. If any capital reorganization or reclassification of the shares of the Company, or consolidation or merger of the Company with another corporation, or the sale of all or substantially all of its assets to another corporation shall be effected in such a way that holders of Common Shares shall be entitled to receive stock, securities, cash or other property with respect to or in exchange for Common Shares, then, as a condition of such reorganization, reclassification, consolidation, merger or sale, lawful and adequate provision shall be made whereby the Holder of this Warrant shall have the right to acquire and receive upon exercise hereof such common stock, securities, cash or other property issuable or payable (as part of the reorganization, reclassification, consolidation, merger or sale) with respect to or in exchange for such number of outstanding Common Shares of the Company as would have been received upon exercise of this Warrant at the Purchase Price then in effect. The Company will not effect any such consolidation, merger or sale unless prior to the consummation thereof the successor corporation (if other than the Company) resulting from such consolidation or merger or the corporation purchasing such assets shall assume by written instrument, mailed or delivered to the Holder of this Warrant at the last address of such Holder appearing on the books of the Company, the obligation to deliver to such holder such common stock, securities or assets as, in accordance with the foregoing provisions, such Holder may be entitled to purchase. In the event that pursuant to the terms of this Paragraph 3.4, this Warrant becomes exercisable for securities other than Common Shares, then the provisions of Section 3 shall apply to such securities as though such securities were Common Shares. If a purchase, tender or exchange offer is made to and accepted by the holders of more than 50% of the outstanding Common Shares of the Company, the Company shall not effect any -7- consolidation, merger or sale with the person having made such offer or with any Affiliate of such person unless prior to the consummation of such consolidation, merger or sale the holder of this Warrant shall have been given a reasonable opportunity to then elect to receive upon the exercise of this Warrant either the common shares, securities or assets then issuable with respect to the Common Shares of the Company or the common shares, securities or assets, or the equivalent, issued to previous holders of the Common Shares in accordance with such offer. For purposes hereof the term "Affiliate" with respect to any given person shall mean any person controlling, controlled by or under common control with the given person. 3.5. No Adjustment for Exercise of Certain Options, Warrants, Etc. The provisions of this Section 3 shall not apply to any Common Shares issued, issuable or deemed outstanding under subparagraphs (1) to (8) of paragraph 3.1, inclusive: (i) to any person pursuant to any stock option, stock purchase or similar plan or arrangement for the benefit of employees or directors of the Company or its subsidiaries; provided that any Common Shares issued pursuant to any such plan or arrangement (in excess of 1,700,000 shares) shall be approved by the Board of Directors or a duly organized committee thereof, it being further provided that, with respect to Class A Warrants exercised by the Initial Investors or their Affiliates (as defined in the Registration Statement filed by the Company in connection with the Company's public offering of its Common Shares), this Section 3 shall apply with respect to any Common Shares issued pursuant to any such plan or arrangement in excess of 1,700,000 shares (ii) pursuant to options, warrants and conversion rights in existence on the date of issuance hereof or (iii) pursuant to the exercise of any Class A Warrants or Class B Warrants described in the Company's prospectus relating to the initial public offering of its Common Shares. 3.6. Notices of Record Date, Etc. In the event that: (1) the Company shall declare any cash dividend upon its Common Shares, or (2) the Company shall declare any dividend upon its Common Shares payable in common shares or make any special dividend or other distribution to the holders of its Common Shares, or (3) the Company shall offer for subscription pro rata to the holders of its Common Shares any additional common shares of any class or other rights, or (4) there shall be any capital reorganization or reclassification of the shares of the Company, including any subdivision or combination of its outstanding Common Shares, or consolidation or merger of the Company with, or sale of all or substantially all of its assets to, another corporation, or (5) there shall be a voluntary or involuntary dissolution, liquidation or winding up of the Company; then, in connection with such event, the Company shall give to the Holder of this Warrant: -8- (i) at least ten (10) days' prior written notice of the date on which the books of the Company shall close or a record shall be taken for such dividend distribution or subscription rights or for determining rights to vote in respect of any such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation or winding up; and (ii) in the case of any such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation or winding up, at least ten (10) days prior written notice of the date when the same shall take place. Such notice in accordance with the foregoing clause (i) shall also specify, in the case of any such dividend, distribution or subscription rights, the date on which the holders of Common Shares shall be entitled thereto, and such notice in accordance with the foregoing clause (ii) shall also specify the date on which the holders of Common Shares shall be entitled to exchange their Common Shares for securities or other property deliverable upon such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation or winding up, as the case may be. Each such written notice shall be given by first class mail, postage prepaid, addressed to the Holder of this Warrant at the address of such Holder as shown on the books of the Company. 3.7. Adjustments for Other Distributions. If at any time or from time to time on or after the date of issuance hereof, the Company shall distribute, grant or issue to all holders of its Common Shares any of its assets or debt securities or any rights or warrants to purchase assets or securities of the Company (including securities or cash, but excluding (x) distributions covered by Section 3.1 or (y) cash dividends or other cash distributions that are paid out of consolidation current net earnings or earnings retained in the business as shown on the books of the Company unless such cash distributions in any twelve month period exceed 3.00% of the average Market Price of the Common Shares for the fifteen (15) trading days ending on the first day of such twelve month period) (collectively, the "Purchase Rights"), then the Holder of this Warrant shall be entitled to, at its option: (i) have the Purchase Price reduced to the Purchase Price (calculated to the nearest tenth of a cent) determined by multiplying the Purchase Price in effect immediately prior to the time of distribution of such Purchase Rights by a fraction, the numerator of which shall be the difference between (x) the Market Price immediately prior to such distribution and (y) the fair market value of the assets, securities, rights or warrants applicable to one Common Share (which fair market value shall be determined by the Company in accordance with generally accepted accounting principals) and the denominator of which shall be the Market Price immediately prior to such distribution; provided that in the case of a distribution, grant or issuance pursuant to a purchase, underwriting or similar agreement, the Market Price shall mean the Market Price in effect upon the date such agreement is executed by the Company; or (ii) acquire (within thirty (30) days after the later to occur of the initial exercise date of such Purchase Rights or receipt by such Holder of the notice concerning Purchase Rights to which such Holder shall be entitled under Para- -9- graph 3.6) and upon the terms applicable to such Purchase Rights either: (x) the aggregate Purchase Rights which such Holder could have acquired if it had held the number of Common Shares acquirable upon exercise of this Warrant immediately before the grant, issuance or sale of such Purchase Rights; provided that if any Purchase Rights were distributed to holders of Common Shares without the payment of additional consideration by such holders, corresponding Purchase Rights shall be distributed to the exercising holder of this Warrant as soon as possible after such exercise and it shall not be necessary for the exercising holder of this Warrant specifically to request delivery of such rights; or (y) in the event that any such Purchase Rights shall have expired or shall expire prior to the end of said thirty (30) day period, the number of Common Shares or the amount of property which such Holder could have acquired upon such exercise at the same time or times at which the Company granted, issued or sold such expired Purchase Rights. 3.8. Adjustment by Board of Directors. If any event occurs as to which the provisions of this Section 3 are not strictly applicable or if strictly applicable would not fairly protect the rights of the Holder of this Warrant in accordance with the essential intent and principles of such provisions, then the Board of Directors shall make an adjustment in the application of such provisions, in accordance with such essential intent and principles, so as to protect such rights as aforesaid, but in no event shall any adjustment have the effect of increasing the Purchase Price as otherwise determined pursuant to any of the provisions of this Section 3 except in the case of a combination of shares of a type contemplated in Paragraph 3.3 and then in no event to an amount larger than the Purchase Price as adjusted pursuant to Paragraph 3.3. 3.9. Fractional Shares. The company shall not issue fractions of Common Shares upon exercise of this Warrant or scrip in lieu thereof. If any fraction of a Common Share would, except for the provisions of this Paragraph 3.9, be issuable upon exercise of this Warrant, the company shall in lieu thereof pay to the person entitled thereto an amount in cash equal to the product of such fraction, calculated to the nearest one-hundredth (1/100), and the Market Price of a Common Share as of such date of exercise. 3.10. Officers' Statement as to Adjustments. Whenever the Purchase Price shall be adjusted as provided in this Section 3, the Company shall forthwith file at the office designated for the exercise of this Warrant a statement, signed by the chairman of the Board, the President, any Vice President or the Treasurer of the Company, showing in reasonable detail the facts requiring such adjustment and the Purchase Price that will be effective after such adjustment. The Company shall also cause a notice setting forth any such adjustments to be sent by mail, first class, postage prepaid, to the record holder of this warrant at his or its address appearing on the Warrant register of the Company. If such notice relates to an adjustment resulting from an event referred to in Paragraph 3.6, such notice shall be included as part of the notice required to be mailed and published under the provisions of Paragraph 3.6. 4. NO DILUTION OR IMPAIRMENT. The Company will not, by amendment of its charter or through reorganization, reclassification, consolidation, amalgamation, merger, dissolution, -10- sale of assets or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of this Warrant, but will at all times in good faith assist in the carrying out of all such terms and in the taking of all such action as may be necessary or appropriate in order to protect the rights of the Holder hereof against dilution or other impairment. Without limiting the generality of the foregoing, the Company will not increase the par value of any Common Share receivable upon the exercise of this Warrant above the amount payable therefor upon such exercise, and at all times will take all such action as may be necessary or appropriate in order that the Company may validly and legally issue fully paid and nonassessable Common Shares upon the exercise of this Warrant. 5. RESERVATION OF COMMON SHARES, ETC., ISSUABLE UPON EXERCISE OF WARRANTS. The Company shall at all times reserve and keep available out of its authorized but unissued Common Shares, solely for issuance and delivery upon the exercise of this Warrant and other similar warrants, such number of its duly authorized Common Shares as from time to time shall be issuable upon the exercise of this Warrant and all other similar warrants at the time outstanding. 6. REPLACEMENT OF WARRANT. Upon receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant and (in the case of loss, theft or destruction) upon delivery of an indemnity agreement (with surety if reasonably required) in an amount reasonably satisfactory to it, or (in the case of mutilation) upon surrender and cancellation thereof, the Company will issue, in lieu thereof, a new Warrant of like tenor. 7. REMEDIES. The Company stipulates that the remedies at law of the Holder of this Warrant in the event of any default by the Company in the performance of or compliance with any of the terms of this Warrant are not and will not be adequate, and that the same may be specifically enforced. 8. NEGOTIABILITY, ETC. This Warrant is issued upon the following terms, to all of which each taker or owner hereof consents and agrees: (a) Nether this Warrant, the Common Shares underlying this Warrant (the "Underlying Stock") nor the rights of the Holder hereunder may be transferred except in compliance with the provisions of a certain Subscription Agreement and a certain Shareholders Agreement executed in connection with the issuance of this Warrant, copies of which are on file at the principal office of the Company. The provisions of this Section 8 shall be binding upon any transferee of this Warrant and upon each holder of Underlying Stock. (b) Subject to the limitation described in this Section 8, title to this Warrant may be transferred by endorsement (by the Holder hereof executing the form of assignment at the end hereof including guaranty of signature) and delivery in the same manner as in the case of a negotiable instrument transferable by endorsement and delivery. -11- (c) Any person in possession of this Warrant properly endorsed and, if not the original holder hereof, to whom possession was transferred in accordance with the provisions was transferred in accordance with the provisions of clauses (a) and (b) of this Section 8 is authorized to represent himself as absolute owner hereof and is granted power to transfer absolute title hereto by endorsement and delivery hereof to a bona fide purchaser hereof for value; each prior taker or owner waives and renounces all of his equities or rights in this Warrant in favor of every such bona fide purchaser, and every such bona fide purchaser shall acquire title hereto and to all rights represented hereby. (d) Until this Warrant is transferred on the books of the Company, the Company may treat the registered Holder of this Warrant as the absolute owner hereof for all purposes without being affected by any notice to the contrary. (e) The Company shall not be required to pay any U.S. federal or state transfer tax or charge that may be payable in respect of any transfer involved in the transfer or delivery of this Warrant or the issuance or conversion or delivery of certificates for Common Shares in a name other than that of the registered Holder of this warrant or to issue or deliver any certificates for Common Shares upon the exercise of this Warrant until any and all such taxes and charges shall have been paid by the Holder of this Warrant or until it has been established to the Company's satisfaction that no such tax or charge is due. 9. NO RIGHTS TO VOTE OR RECEIVE DIVIDENDS OR OTHER DISTRIBUTIONS. Prior to the exercise of this Warrant, the Holder hereof shall not be entitled to any rights of a shareholder of the Company with respect to Common Shares for which this Warrant shall be exercisable, including, without limitation, the right to vote, to receive dividends or other distributions or to exercise any preemptive rights, and shall not be entitled to receive any notice of any proceedings of the Company, except as provided herein. 10. MAILING OF NOTICES, ETC. All notices and other communications from the Company to the Holder of this Warrant shall be mailed by first-class certified mail, postage prepaid, to the address furnished to the Company in writing by the last Holder of this Warrant who shall have furnished an address to the Company in writing. 11. CHANGE, WAIVER, ETC. The terms of this Warrant may not be changed, waived, discharged or terminated orally but only by an instrument in writing signed by the Holder of this Warrant against which enforcement of the change, waiver, discharge or termination is sought. 12. GOVERNING LAW. This Warrant shall be governed by and construed in accordance with the laws of Bermuda, without regard to principles regarding conflicts of laws. S-1 ARCH CAPITAL GROUP LTD. By: ------------------------------------- Name: Title: Dated: Attest: [To be signed only upon exercise of Warrant] To Arch Capital Group Ltd. The undersigned, the Holder of the within Warrant, hereby irrevocably elects to exercise the purchase right represented by such Warrant for, and to purchase thereunder, ________________ Common Shares of Arch Capital Group Ltd. and herewith makes payment of $_________ therefor and/or requests that the number of Common Shares for which the within Warrant is exercisable to reduced by __________ Common Shares (in addition to the Common Shares being purchased) and/or delivers _________ Common Shares, the aggregate of such payment being equal to the aggregate purchase price for the Common Shares being purchased, and requests that the certificates for the Common Shares being purchased be issued in the name of, and be delivered to, _____________, whose address is - ----------------. Dated: _______________________________ ______________________________________________ (Signature must conform in all respects to name of Holder as specified on the face of the Warrant) ______________________________________________ Address [To be signed only upon transfer of Warrant] FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers unto ______________ the within Warrant and appoints _______________ attorney to transfer said right on the books of Arch Capital Group Ltd. with full power of substitution in the premises. Dated: _____________________________ _______________________________________________ (Signature must conform in all respects to name of Holder as specified on the face of the Warrant) _______________________________________________ Address In the presence of _____________________________