Exhibit 10.1

NONQUALIFIED STOCK OPTION AGREEMENT

This AGREEMENT (this “Agreement”) is made as of June 29, 2010 (the “Effective Date”) by and between HealthMarkets, Inc., a Delaware corporation (the “Company”), and Jack Victor Heller (“Optionee”). As a condition precedent to the Company’s grant of the Options (as defined in Section 2 of this Agreement) to Optionee, to the extent not already executed by Optionee, Optionee is required to execute and deliver a counterpart of the Stockholders Agreement and thereby agrees to be bound by the Stockholders Agreement as a “Management Stockholder” thereunder.

1. Certain Definitions. Capitalized terms used, but not otherwise defined, in this Agreement will have the meanings given to such terms in the Company’s Second Amended and Restated 2006 Management Option Plan (the “Plan”). As used in this Agreement:

(a) “Call Right” has the meaning specified in Section 8 of this Agreement.

(b) “Company” has the meaning specified in the introductory paragraph of this Agreement.

(c) “Compensation Committee” means the Executive Compensation Committee of the Board.

(d) “Disability” means, unless defined otherwise in the applicable Employment Agreement, Optionee’s incapacity due to physical or mental illness to substantially perform his duties on a full-time basis for at least 26 consecutive weeks or an aggregate period in excess of 26 weeks in any one fiscal year, and within 30 days after a notice of termination is thereafter given by the Company, Optionee shall not have returned to the full-time performance of Optionee’s duties; provided, however, that if Optionee shall not agree with a determination to terminate his employment because of Disability, the question of Optionee’s Disability shall be subject to the certification of a qualified medical doctor selected by the Company or its insurers and acceptable to Optionee or, in the event of Optionee’s incapacity to accept a doctor, Optionee’s legal representative.

(e) “Employment Agreement” means an employment agreement or offer letter, if any, with respect to Optionee’s employment with the Company and certain related terms, by and between the Company and Optionee.

(f) “Fair Market Value” shall have the meaning specified in the Stockholders Agreement.

(g) “Options” has the meaning specified in Section 2 of this Agreement.

(h) “Optionee” has the meaning specified in the introductory paragraph of this Agreement.

(i) “Option Price” has the meaning specified in Section 2 of this Agreement.

(j) “Plan” has the meaning specified in Section 1 of this Agreement.

(k) “Termination for Cause” means, unless defined otherwise in the applicable Employment Agreement, the termination by the Company or any Subsidiary of Optionee’s employment with the Company or any Subsidiary as a result of (i) the commission by Optionee of an act of gross negligence, willful misconduct, fraud, embezzlement, misappropriation or breach of fiduciary duty

against the Company or any of its affiliates or Subsidiaries, or the conviction of Optionee by a court of competent jurisdiction of, or a plea of guilty or nolo contendere to, any felony or any crime involving moral turpitude or any crime which reasonably could affect the reputation of the Company or Optionee’s ability to perform the duties required under his Employment Agreement, if any, with the Company or any Subsidiary, (ii) the commission by Optionee of a material breach of any of the covenants in his Employment Agreement, if any, with the Company or any Subsidiary or the Stockholders Agreement, which breach has not been remedied within 30 days of the delivery to Optionee by the Board of written notice of the facts constituting the breach, and which breach if not cured, would have a material adverse effect on the Company, or (iii) the habitual and willful neglect by Optionee of his obligations under his Employment Agreement, if any, with the Company or any Subsidiary or Optionee’s duties as an employee of the Company or any Subsidiary.

(l) “Termination for Good Reason” means, unless defined otherwise in the applicable Employment Agreement, the termination by Optionee of Optionee’s employment with the Company or any Subsidiary with written notice to the Company within 90 days following the occurrence, without Optionee’s consent, of any of the following events (after failure of the Company or any Subsidiary to cure in thirty (30) days): (i) the reduction of Optionee’s position from that of an executive level position with the Company or any Subsidiary, (ii) a decrease in Optionee’s base salary or target annual bonus, other than in the case of a decrease for a majority of similarly situated executives of the Company or any Subsidiary, (iii) a reduction in Optionee’s participation in the Company’s or any Subsidiary’s benefit plans and policies to a level materially less favorable to Optionee, unless such reduction applies to a majority of the similarly situated executives of the Company or any Subsidiary, or (iv) the announcement of the relocation of Optionee’s primary place of employment to a location 50 or more miles from the current headquarters or, if Optionee is not currently based at the Company’s current headquarters, Optionee’s primary place of employment as of the Effective Date.

(m) “Termination Without Cause” means, unless defined otherwise in the applicable Employment Agreement, the termination by the Company or any Subsidiary of Optionee’s employment with the Company or any Subsidiary for any reason other than a Termination for Cause (other than by reason of Optionee’s death or Disability).

(n) “Voluntary Termination” means Optionee’s termination of Optionee’s employment with the Company or any Subsidiary for any reason, other than a Termination for Good Reason.

2. Grant of Stock Option; Exercise Price.

(a) Subject to and upon the terms, conditions, and restrictions set forth in this Agreement and in the Plan, the Company hereby grants to Optionee options to purchase 150,000 Shares (the “Options”) as of the date hereof. The Shares subject to the Option may be purchased pursuant to the Options at a price (the “Option Price”) of $7.00 per Share. The Options may be exercised from time to time in accordance with the terms of this Agreement. The Options are intended to be nonqualified stock options and shall not be treated as an “incentive stock option” within the meaning of that term under Section 422 of the Code, or any successor provision thereto.

(b) In connection with, and as a condition precedent to, the Company’s grant of the Options set forth in Section 2(a) above, Optionee acknowledges and agrees to forfeit all of his or her outstanding Options granted prior to the date hereof.

3. Term of Options. The term of the Options shall commence at the Effective Date and, unless earlier terminated in accordance with the terms of this Agreement, shall expire ten (10) years from the Effective Date.

4. Right to Exercise. Unless terminated as hereinafter provided and except as otherwise provided in Section 7, the Options shall vest and become exercisable in equal 20% installments on each of the first five anniversaries of the Effective Date, in each case, subject to Optionee remaining in the continuous employ of the Company or any Subsidiary through the applicable vesting date. Notwithstanding the foregoing, the Options granted hereby shall become immediately exercisable with respect to all of the Shares upon the occurrence of a Change of Control if Optionee remains in the continuous employ of the Company or any Subsidiary until the date of the consummation of such Change of Control.

5. Option Nontransferable. Optionee may not transfer or assign all or any part of the Options other than by will or by the laws of descent and distribution. The Options may be exercised, during the lifetime of Optionee, only by Optionee, or in the event of Optionee’s legal incapacity, by Optionee’s guardian or legal representative acting on behalf of Optionee in a fiduciary capacity under state law and court supervision. Optionee shall be entitled to the privileges of ownership with respect to Shares purchased and delivered to Optionee upon the exercise of all or part of the Options.

6. Notice of Exercise; Payment.

(a) To the extent then exercisable, the Option may be exercised in whole or in part by written notice to the Company stating the number of Shares for which the Options are being exercised and the intended manner of payment. The date of such notice shall be the exercise date. Payment equal to the aggregate Option Price of the Shares being purchased pursuant to an exercise of the Options must be tendered in full with the notice of exercise to the Company in one or a combination of the following methods as specified by Optionee in the notice of exercise: (i) cash in the form of currency or check or by wire transfer as directed by the Company, (ii) solely following an IPO on shares of the Company’s Class A-1 Common Stock otherwise being traded on an established securities market, through the surrender to the Company of shares of Class A-1 Common Stock owned by Optionee for at least six months as valued at their Fair Market Value on the date of exercise or (iii) through such other form of consideration as is deemed acceptable by the Board.

(b) As soon as practicable upon the Company’s receipt of Optionee’s notice of exercise and payment, the Company shall direct the due issuance of the Shares so purchased.

(c) As a further condition precedent to the exercise of the Options in whole or in part, Optionee shall comply with all regulations and the requirements of any regulatory authority having control of, or supervision over, the issuance of the Shares and in connection therewith shall execute any documents which the Board shall in its sole discretion deem necessary or advisable.

7. Termination of Employment.

(a) General. Except as provided immediately below, if Optionee’s employment terminates for any reason, the Options, to the extent not then vested (i.e., exercisable), will be immediately forfeited and all vested Options will remain exercisable for the shorter of (1) 90 days following the date of termination and (2) the remainder of their original scheduled term. For the avoidance of doubt, any reference to any Option being or becoming vested shall also mean it has become or will become “exercisable”.

(b) Without Cause; for Good Reason. If Optionee’s employment with the Company or any Subsidiary terminates for any reason other than a Termination for Cause or a Voluntary Termination, to the extent not previously cancelled or expired, as of the date of termination Optionee’s unvested Options that would have vested if Optionee had remained employed through the first anniversary of the date of termination will vest and all vested Options will remain exercisable for the shorter of (1) one year following the date of termination and (2) the remainder of their original scheduled term.

(c) Death; Disability. If Optionee’s employment is terminated by reason of Optionee’s death or Disability, to the extent not previously cancelled or expired, as of the date of termination Optionee’s unvested Options that would have vested if Optionee had remained employed through the first anniversary of the date of termination will vest and all vested Options will remain exercisable for the shorter of (1) one year following the date of termination and (2) the remainder of their original scheduled term; provided, however, that it shall be a condition to the exercise of the Options in the event of Optionee’s death that the Person exercising the Options shall (i) have agreed in a form satisfactory to the Company to be bound by the provisions of this Agreement and the Stockholders Agreement and (ii) comply with all regulations and the requirements of any regulatory authority having control of, or supervision over, the issuance of the Shares and in connection therewith shall execute any documents which the Board shall in its sole discretion deem necessary or advisable.

(d) Cause. Notwithstanding the foregoing or any provision of this Agreement or the Employment Agreement to the contrary, if Optionee’s employment is terminated by the Company for Cause, all options, whether or not vested, will be immediately forfeited as of the date of termination.

8. Company Repurchase Rights.

(a) Upon termination of Optionee’s employment for any reason prior to an IPO, the Company will have the right to purchase (the “Call Right”), subject to the provisions of Section 8(b) below, any Shares that Optionee received pursuant to the terms and conditions set forth in Article VI Call Rights of the Stockholders Agreement.

(b) Notwithstanding anything in the Stockholders Agreement or the Employment Agreement to the contrary, in the event that Optionee is required to repay unvested cash bonus amounts paid to Optionee by the Company, the Company shall have the right to reduce the purchase price payable to Optionee with respect to any Shares held by Optionee by the amount owed to the Company by Optionee with respect to such unvested cash bonus amounts.

(c) This Section 8 shall be deemed an amendment to the terms of the Stockholders Agreement to the extent necessary to effectuate the terms of this Section 8. By executing this Agreement, Optionee agrees to be bound by the terms of the Stockholders Agreement, as modified by this Agreement, and accepts the rights and obligations set forth therein.

9. Initial Public Offering. Shares acquired on exercise of any Option will be subject to the terms and conditions of the Stockholders Agreement. The Company and Optionee acknowledge that they will agree to provide the Company with the right to require Optionee and other executives of the Company or any Subsidiary to waive any registration rights with regard to such Shares upon an IPO, in which case the Company will implement an IPO bonus plan in cash, stock or additional options to compensate for Optionee’s and the other executives’ loss of liquidity.

10. No Employment Contract. Nothing contained in this Agreement shall (a) confer upon Optionee any right to be employed by or remain employed by the Company or any Subsidiary, or (b) limit or affect in any manner the right of the Company or any Subsidiary to terminate the employment or adjust the compensation of Optionee.

11. Taxes and Withholding. The Company or any Subsidiary may withhold, or require Optionee to remit to the Company or any Subsidiary, an amount sufficient to satisfy federal, state, local or foreign taxes (including Optionee’s FICA obligation) in connection with any payment made or benefit realized by Optionee or other person under this Agreement or otherwise, and the amounts available to the Company or any Subsidiary for such withholding are insufficient, it shall be a condition to the receipt of such payment or the realization of such benefit that Optionee or such other person make arrangements satisfactory to the Company or any Subsidiary for payment of the balance of such taxes required to be withheld. The Company or any Subsidiary may elect to have such withholding obligation satisfied by having Optionee surrender to the Company or any Subsidiary a portion of the Shares that is issued or transferred to Optionee upon the exercise of an Option (but only to the extent of the minimum withholding required by law), and the Shares so surrendered by Optionee shall be credited against any such withholding obligation at the Fair Market Value of such shares on the date of such surrender.

12. Compliance with Law. The Company shall make reasonable efforts to comply with all applicable federal and state securities laws; provided, however, that notwithstanding any other provision of this Agreement, the Options shall not be exercisable if the exercise thereof would result in a violation of any such law.

13. Adjustments. In the event of any event described in Section 9 of the Plan occurring after the Effective Date, the adjustment provisions as provided for under Section 9 of the Plan shall apply.

14. Relation to Other Benefits. Any economic or other benefit to Optionee under this Agreement shall not be taken into account in determining any benefits to which Optionee may be entitled under any profit-sharing, retirement or other benefit or compensation plan maintained by the Company or any Subsidiary and shall not affect the amount of any life insurance coverage available to any beneficiary under any life insurance plan covering employees of the Company or any Subsidiary.

15. Amendments. Any amendment to the Plan shall be deemed to be an amendment to this Agreement to the extent that the amendment is applicable hereto; provided, however, that no amendment shall adversely affect the rights of Optionee under this Agreement without Optionee’s written consent.

16. Severability. If one or more of the provisions of this Agreement is invalidated for any reason by a court of competent jurisdiction, any provision so invalidated shall be deemed to be separable from the other provisions hereof, and the remaining provisions hereof shall continue to be valid and fully enforceable.

17. Relation to Plan. This Agreement is subject to the terms and conditions of the Plan. In the event of any inconsistent provisions between this Agreement and the Plan, the Plan shall govern. The Board acting pursuant to the Plan, as constituted from time to time, shall, except as expressly provided otherwise herein, have the right to determine any questions which arise in connection with the Option or its exercise.

18. Successors and Assigns. The provisions of this Agreement shall inure to the benefit of, and be binding upon, the successors, administrators, heirs, legal representatives and assigns of Optionee, and the successors and assigns of the Company.

19. Governing Law. The interpretation, performance, and enforcement of this Agreement shall be governed by the laws of the State of Delaware, without giving effect to the principles of conflict of laws thereof and all parties, including their successors and assigns, consent to the jurisdiction of the state and federal courts of Delaware.

20. Prior Agreement. As of the date Optionee countersigns this Agreement, this Agreement will supersede any and all prior and/or contemporaneous agreements, either oral or in writing, between the parties hereto, or between either or both of the parties hereto and the Company, with respect to the subject matter hereof, including, without limitation, the Employment Agreement, if applicable. Each party to this Agreement acknowledges that no representations, inducements, promises, or other agreements, orally or otherwise, have been made by any party, or anyone acting on behalf of any party, pertaining to the subject matter hereof, which are not embodied herein, and that no prior and/or contemporaneous agreement, statement or promise pertaining to the subject matter hereof that is not contained in this Agreement shall be valid or binding on either party.

21. Notices. For all purposes of this Agreement, all communications, including without limitation notices, consents, requests or approvals, required or permitted to be given hereunder will be in writing and will be deemed to have been duly given when hand delivered or dispatched by electronic facsimile transmission (with receipt thereof confirmed), or five business days after having been mailed by United States registered or certified mail, return receipt requested, postage prepaid, or three business days after having been sent by a nationally recognized overnight courier service such as Federal Express, UPS, or Purolator, addressed to the Company (to the attention of the Secretary of the Company) at its principal executive offices and to Optionee at his principal residence, or to such other address as any party may have furnished to the other in writing and in accordance herewith, except that notices of changes of address shall be effective only upon receipt.

22. Counterparts. This Agreement may be executed in one or more counterparts, each of which shall be deemed to be an original but all of which together will constitute one and the same agreement.

IN WITNESS WHEREOF, the Company has caused this Agreement to be executed on its behalf by its duly authorized officer and Optionee has executed this Agreement, as of the day and year first above written.