EMPLOYMENT AND NON-COMPETITION AGREEMENT

Exhibit 10.2

EMPLOYMENT AND NON-COMPETITION AGREEMENT

This AGREEMENT is effective this the 1st day of September, 2002 between PROSPERITY BANK, a Texas banking association, having a principal place of business at 1301 N. Mechanic, El Campo, Texas 77437 hereinafter referred to as “Employer,” and PETER E. FISHER who resides in Spring, Texas 33739, hereinafter referred to as “Employee” (the “Agreement”). Prosperity Bancshares, Inc. is also executing this Agreement as guarantor of the obligations under this Agreement of its subsidiary, Prosperity Bank.

ARTICLE I

TERM OF EMPLOYMENT

Employer hereby employs Employee and Employee hereby accepts employment with Employer for a period of two (2) years (the “Term”) beginning on the Closing Date (as that term is defined in that certain Agreement and Plan of Reorganization dated as of May 1, 2002 by and between Prosperity Bancshares, Inc. and Paradigm Bancorporation, Inc.) (referred to herein as the “Effective Date”); provided, however, that this Agreement may be terminated earlier as hereinafter provided.

ARTICLE II

DUTIES OF EMPLOYEE

2.1 Primary Duties. Employee is hereby employed by Employer as Vice Chairman of Prosperity Bank and shall primarily manage the solicitation and servicing of loan and depository accounts of Employer associated with the locations of Employer which were previously those of Paradigm Bank Texas and shall perform such other work as may be assigned to him subject to the instructions, directions, and control of Employer, which shall be consistent with the type of nature of work normally performed by senior banking officers.

2.2 Location. Employee shall work in Houston, Texas and shall be furnished with an office and other business facilities and services sufficient to carry out his duties of office.

2.3 Changes of Duties or Location-Mutual Consent. The duties of Employee and the location at which employee shall work may be changed from time to time by the mutual consent of Employer and Employee without resulting in a rescission of this Agreement.

Notwithstanding any such change, the employment of Employee shall be construed as continuing under this Agreement as modified.

ARTICLE III

ENGAGING IN OTHER EMPLOYMENT

Employee shall devote all of his entire productive time, ability, and attention to the business of Employer during Employer’s normal business hours, and Employee shall not directly or indirectly render any services of a business, commercial, or professional nature relating to

banking or financial matters to any other person or organization, whether for compensation or otherwise, without prior written consent of Employer during the Term of this Agreement and during the non-competition period described in Article VI below.

ARTICLE IV

COMPENSATION

4.1 Base Salary. As compensation for employment services rendered under this Agreement, Employee shall be entitled to receive from Employer an annual salary (“Base Salary”) of $185,000.00, prorated for any partial employment period during the two (2) year Term of this Agreement. The Base Salary shall be subject to review in accordance with the then existing procedures of Employer.

4.2 Bonus. Employer will guarantee a bonus payment of not less than $15,000.00 (“Bonus”) for each year of the Term of the Agreement, to be paid in accordance with Employer’s policies and procedures regarding annual bonuses.

4.3 Options. On the Effective Date of this Agreement, Employer shall deliver to Employee an incentive stock option agreement issued pursuant to the Prosperity Bancshares, Inc. 1998 Stock Incentive Plan (“Prosperity Stock Incentive Plan”) granting to Employee options to purchase 30,000 shares of common stock of Employer pursuant to the Prosperity Stock Incentive Plan. Subject to Section 8.2.3 hereof, the options shall vest twenty percent (20%) per annum beginning on the second anniversary of the grant date, shall have a term of 10 years and shall otherwise be subject to the terms and conditions of the Prosperity Stock Incentive Plan.

ARTICLE V

REIMBURSEMENT OF EMPLOYEE BUSINESS EXPENSES AND

PARTICIPATION IN EMPLOYER BENEFIT PLANS

5.1 Out of Pocket Expenses; Club Dues. Employee is authorized to incur reasonable business expenses for promoting the business of Employer, including expenditures for entertainment and travel, including, without limitation, trade association convention attendance, country club dues, mobile telephone expenses, and other similar business expenses. Employer and Employee will mutually determine a reasonable range for such business expenses. Employer will reimburse Employee from time to time for all such business expenses provided that Employee presents Employer with appropriate documentation of such expenditures in accordance with Employer’s established procedures relating to such reimbursements. During the Term of this Agreement, Employer will reimburse Employee for Employee’s membership dues at the University Club, Houston, Texas.

5.2 Participation in Employer Benefit Plans. Until the termination of Employee’s employment, Employee will be eligible to participate in all employee benefit plans generally available to the officers and employees of Employer in accordance with the terms of such plans.

-2-

5.3 Automobile Allowance. During the Term of this Agreement, Employer shall provide Employee with a monthly automobile allowance of $800, which shall be paid through the normal payroll practices of Employer.

ARTICLE VI

NON-DISCLOSURE, NON-COMPETITION AND NON-SOLICITATION COVENANTS

6.1 Non-Disclosure Obligations. “Confidential Information” means and includes Employer’s confidential and/or proprietary information and/or trade secrets that have been and/or will be developed or used and that cannot be obtained readily by third parties from outside sources. Confidential Information includes, but is not limited to, the following: information regarding customers, employees, contractors, and the industry not generally known to the public; strategies, methods, books, records, and documents; technical information concerning products, equipment, services, and processes; procurement procedures, pricing, and pricing techniques; information concerning past, current, and prospective customers, investors, and business affiliates (such as contact name, service provided, pricing, type and amount of services used, financial data, and/or other such information); pricing strategies and price curves; positions; plans or strategies for expansion or acquisitions; budgets; research; financial and sales data; trading methodologies and terms; communications information; evaluations, opinions, and interpretations of information and data; marketing and merchandising techniques; electronic databases; models; specifications; computer programs; contracts; bids or proposals; technologies and methods; training methods and processes; organizational structure; personnel information; payments or rates paid to consultants or other service providers; and other such confidential or proprietary information. Employee acknowledges that Employer’s business is highly competitive, that this Confidential Information constitutes a valuable, special, and unique asset used by Employer in its business, and that protection of such Confidential Information against unauthorized disclosure and use is of critical importance to Employer.

Employee agrees that Employee will not, at any time during or after Employee’s employment with Employer, make any unauthorized disclosure, directly or indirectly, of any Confidential Information of Employer, or third parties, or make any use thereof, directly or indirectly, except in working for Employer. Employee also agrees that Employee shall deliver promptly to Employer at the termination of employment or at any other time at Employer’s request, without retaining any copies, all documents and other material in Employee’s possession relating, directly or indirectly, to any Confidential Information or other information of Employer, or Confidential Information or other information regarding third parties, learned as an employee at Employer.

6.2 Non-Competition Obligations. Immediately upon Employee’s signing of this Agreement, Employer shall provide Employee with Confidential Information. Ancillary to the consideration to be provided pursuant to Section 6.3 hereof, including but not limited to Employer’s agreement to provide Confidential Information to Employee and Employee’s agreement not to disclose Confidential Information, and in order to protect the Confidential Information, Employer and Employee agree to the following non-competition provisions.

6.2.1 Employee Obligations. Employee agrees that, during the term of Employee’s employment with Employer, which may exceed the Term of this Agreement, and for

-3-

the periods set forth in Section 6.2.2 below, Employee will not, except as an employee of Employer, in any capacity for Employee or others, directly or indirectly:

(a) compete or engage, anywhere in the geographic area comprised of Houston, Texas and the fifty (50) mile radius surrounding Houston, Texas (the “Market Area”), in a business similar to that of Employer, or compete or engage in that type of business which Employer has plans to engage in, or any business which Employer has engaged in during the preceding twelve (12) month period if within the twenty-four (24) months before the termination of Employee’s employment, Employee had access or potential access to information regarding the proposed plans or the business in which Employer engaged;

(b) take any action to invest in, own, manage, operate, control, participate in, be employed or engaged by or be connected in any manner with any partnership, corporation or other business or entity engaging in a business similar to that of Employer anywhere within the Market Area. Notwithstanding the foregoing, the Employee is permitted hereunder to own, directly or indirectly, up to one percent (1%) of the issued and outstanding securities of any publicly traded financial institution conducting business in the Market Area;

(c) call on, service, or solicit competing business from customers or prospective customers of Employer if, within the twenty-four (24) months before the termination of Employee’s employment, Employee had or made contact with the customer, or had access to information and files about the customer; or

(d) call on, solicit, or induce any employee of Employer whom Employee had contact with, knowledge of, or association with in the course of employment with Employer to terminate employment from Employer, and will not assist any other person or entity in such activities.

6.2.2 Non-Competition Period. The Non-Competition Obligations set forth in this Section 6.2 shall apply for a period of twenty-four (24) months after the termination of Employee’s employment with Employer (“Non-Competition Period”), regardless of whether such termination occurs prior to or following the expiration of the Term of this Agreement.

6.2.3 Use of Confidential Information. Employee agrees that Employee’s work for Employer’s competitor during the Non-Competition Period after termination of employment inevitably would lead to Employee’s unauthorized use of Employer’s Confidential Information, even if such use is unintentional. Because it would be impossible, as a practical matter, to monitor, restrain, or police Employee’s use of such Confidential Information other than by Employee’s not working for a competitor, Employee agrees that restricting such employment as set forth in this Agreement is the narrowest way to protect Employer’s interests, and the narrowest way of enforcing Employee’s consideration for the receipt of Employer’s specialized training and Confidential Information (namely, Employee’s promise not to use or disclose that Confidential Information and/or specialized training).

6.2.4 Early Resolution Conference. The parties are entering into this Agreement with the understanding that this Agreement is clear and enforceable. If Employee decides to contend that any restriction on activities under this Agreement is not enforceable or

-4-

does not apply to an activity Employee intends to pursue, Employee first will notify the Chief Executive Officer of Employer in writing and meet with an Employer representative at least fourteen days before engaging in any activity that foreseeably could fall within the questioned restriction to discuss the resolution of such claims (an “Early Resolution Conference”). Should the parties not resolve the dispute at the Early Resolution Conference, the parties may pursue legal recourse. Employer and Employee acknowledge and agree that breach of any of the covenants made by Employee herein would cause irreparable injury to Employer, which could not sufficiently be remedied by monetary damages; and, therefore, that Employer shall be entitled to obtain such equitable relief as declaratory judgments; temporary, preliminary, and permanent injunctions; and order of specific performance to enforce those covenants or to prohibit any act or omission that constitutes a breach thereof. If Employer must bring suit to enforce this Agreement, Employer is entitled to recover its attorneys’ fees and costs related thereto.

6.2.5 Tolling. In the event that Employer shall file a lawsuit in any Court of competent jurisdiction alleging a breach of any of Employee’s obligations under this Agreement, then any time period set forth in this Agreement, including the time periods set forth above, shall be deemed tolled as of the time such lawsuit is filed and shall remain tolled until such dispute finally is resolved either by written settlement agreement resolving all claims raised in such lawsuit or by entry of a final judgment in such lawsuit and the final resolution of any post-judgment appellate proceedings.

6.3 Consideration. In consideration for the above obligations of the Employee, Employer agrees to provide Employee with immediate access to Confidential Information relating to Employer’s business and to highly specialized training regarding Employer’s methodologies and business strategies, which will enable Employee to perform his or her job for Employer. Employee also will have immediate access to, or knowledge of, new Confidential Information of third parties, such as actual and potential customers, suppliers, partners, joint venturers, investors, financing sources, etc., of Employer. In addition, in exchange for Employee’s promises under this Article VI and in accordance with the terms hereof, Employer will pay Employee a non-competition payment (“Non-Competition Payment”) of $100,000.

6.4 Enforcement and Legal Remedies. The parties recognize the difficulty of properly measuring the damages which reasonably would accrue by reason of a breach of this covenant of non-competition and therefore agree that the party suffering by reasons of any breach of this Agreement shall be entitled to the equitable remedy of injunctive relief.

ARTICLE VII

PROPERTY RIGHTS

7.1 Trade Secrets and Confidentiality. During the term of employment, Employee will have access to and become familiar with Confidential Information owned by Employer and regularly used in the operation of the business of Employer. Employee shall not disclose any such Confidential Information, directly or indirectly, nor use it in any way, either during the term of this Agreement or at any time thereafter, except as required in the course of his employment with Employer. All Confidential Information and similar items relating to the business of

-5-

Employer, whether or not prepared by Employee, shall remain the exclusive property of Employer and shall not be removed from the premises of Employer under any circumstances without the prior written consent of Employer, provided, however, that Employee may remove such items for the purpose of furthering the business of Employer if such action is consistent with the past practices of Employee. All items removed from the premises of Employer and all copies or summaries thereof shall be returned to Employer upon the termination of Employee.

7.2 Processes and Improvements. Employee agrees that he will promptly from time to time fully inform and disclose to Employer all inventions, processes, designs, improvements and discoveries which he now has or may hereafter have during the term of this Agreement which pertain or relate to the business of Employer or to any experimental work carried on by Employer, whether conceived by Employee alone or with others and whether or not conceived during regular working hours. All such processes, designs, improvements, formulas, business plans, technologies and discoveries shall be the exclusive property of Employer.

ARTICLE VIII

TERMINATION RIGHTS

8.1 Employee’s Termination Rights. Employee shall have the right, at his election and for any reason prior to the expiration of the Term of this Agreement, to voluntarily terminate his employment with Employer. In the event of such voluntary termination of employment by Employee, Employer’s obligations to pay the Base Salary and Bonus shall automatically cease, except that any accrued but unpaid Base Salary and other benefits shall be paid through the date of such termination, the Non-Competition Payment shall be paid within 30 days following termination and both parties’ obligations set forth in Article VI shall continue.

8.2 Employer’s Termination Rights. Employer shall have the right to terminate Employee at its election and for any reason, with or without Good Cause, prior to the expiration of the Term of this Agreement.

8.2.1 In the event of the death of Employee, Employer’s obligations to pay the Base Salary and Bonus and both parties’ obligations set forth in Article VI shall automatically cease, except that any accrued but unpaid Base Salary and other benefits shall be paid through the date of such termination.

8.2.2 In the event of termination of Employee for Good Cause, Employer’s obligations to pay the Base Salary and Bonus shall automatically cease, the Non-Competition Payment shall be paid within 30 days following termination and both parties’ obligations set forth in Article VI shall continue. Any accrued but unpaid Base Salary and other benefits shall be paid through the date of such termination.

8.2.3 In the event of the termination of Employee without Good Cause, Employer shall pay the remaining Base Salary and Bonus through the Term of this Agreement, the stock options granted pursuant to Section 4.3 hereof shall vest and become immediately exercisable, the Non-Competition Payment shall be paid within 30 days following termination and both parties’ obligations set forth in Article VI shall continue.

-6-

8.3 Definition of Good Cause. For purposes of this Agreement, “Good Cause” shall mean:

(a) Employee’s repeated failure to perform his duties under Section 2.1 of this Agreement;

(b) Employee’s repeated violation of Employer’s written policies and procedures; provided that the terms of this Agreement shall control in the event of any conflict between such policies and procedures and the terms of this Agreement;

(c) use of alcohol or drugs that prevents Employee from performing his duties under Section 2.1 of this Agreement;

(d) conviction of a felony, or conviction of a misdemeanor involving active and willful fraud or moral turpitude; or

(e) acts of disloyalty to Prosperity Bancshares, Inc. or Employer, including, but not limited to, theft, embezzlement or intentional unauthorized disclosure of Confidential Information.

ARTICLE IX

GENERAL PROVISIONS

9.1 Notices. Any notices to be given hereunder by either party to the other may be effected either by personal delivery in writing or by mail, registered or certified, postage prepaid with return receipt requested. Mailed notices shall be addressed to the parties at the addresses appearing in the introductory paragraph of the Agreement, but each party may change his address by written notice in accordance with this paragraph. Notices delivered personally shall be deemed communicated as of actual receipt; mailed notices shall be deemed communicated as of three (3) days after mailing.

9.2 Entire Agreement. This Agreement supersedes any and all other agreements, either oral or in writing, between the parties hereto with respect to the employment of Employee by Employer and contains all of the covenants and agreements between the parties with respect to such employment in any manner whatsoever.

9.3 Governing Law. This Agreement shall be governed by and construed in accordance with the laws of the State of Texas.

9.4 Modification. This Agreement shall not be amended, modified, or altered in any manner except in writing signed by both parties.

9.5 Failure to Enforce Not Waiver. Any failure or delay on the part of either Employer or Employee to exercise any remedy or right under this Agreement shall not operate as a waiver. The failure of either party to require performance of any of the terms, covenants, or provisions of this Agreement by the other party shall not constitute a waiver of any of the rights under the Agreement. No forbearance by either party to exercise any rights or privileges under

-7-

this Agreement shall be construed as a waiver, but all rights and privileges shall continue in effect as if no forbearance had occurred. No covenant or condition of this Agreement may be waived except by the written consent of the waiving party. Any such written waiver of any term of this Agreement shall be effective only in the specific instance and for the specific purpose given.

9.6 Survival. Nothwithstanding anything in this Agreement to the contrary, the provisions of Article VI hereof shall survive early termination or expiration of the Term of this Agreement.

9.7 Partial Invalidity. If any provision of this Agreement is held by a court of competent jurisdiction to be invalid, void, or unenforceable, the remaining provisions shall remain in full force and effect, as if this Agreement has been executed without any such invalid provisions having been included. Such invalid provision shall be reformed in a manner that is both (i) legal and enforceable, and (ii) most closely represents the parties’ original intent.

9.8 Attorney’s Fees and Costs. If any action at law or in equity is necessary to enforce or interpret the terms of this Agreement, the prevailing party shall be entitled to reasonable attorney’s fees, costs, and necessary disbursements in addition to any other relief to which he may be entitled.

9.9 Counterparts. This Agreement may be executed in multiple counterparts, each of which shall be deemed an original, and all of which shall constitute one and the same instrument.

9.10 Successors and Assigns. This Agreement shall be binding upon and shall inure to the benefit of Employer and Employee, and their respective heirs, executors, administrators, successors and assigns, including, without limitation, any successor by merger, consolidation or stock purchase of Employer and any entity or person that acquires all or substantially all of the assets of Employer.

[Signature Page Follows.]

-8-

IN WITNESS WHEREOF, the parties hereto have caused this Employment and Non-Competition Agreement to be duly executed and effective as of the date first written above.

-9-