WARRANT EXERCISE AGREEMENT

Exhibit 10.1

WARRANT EXERCISE AGREEMENT

This Warrant Exercise Agreement (this “Agreement”), dated as of March 5, 2015, is by and among Capnia, Inc., a Delaware corporation (the “Company”), and the undersigned holder (the “Holder”) of one or more Series B Warrants to purchase shares of Common Stock (the “Existing Warrants”) issued by the Company on November 18, 2014 pursuant to the Series B Warrant Agreement dated as of November 18, 2014 by and among the Company and American Stock Transfer and Trust Company as warrant agent (the “Existing Warrant Agreement”).

WHEREAS, the Holder agrees to immediately exercise their Existing Warrants, pursuant to the terms set forth therein, and in consideration therefor, the Holder shall receive newly issued Common Stock Purchase Warrants from the Company pursuant to the terms set forth herein (the “Series C Warrants”);

NOW, THEREFORE, IN CONSIDERATION of the mutual covenants contained in this Agreement, and for good and valuable consideration the receipt and adequacy of which are hereby acknowledged, the Holder and the Company agree as follows:

ARTICLE I

DEFINITIONS

Section 1.1 Definitions.

(a) Capitalized terms not defined in this Agreement shall have the meanings ascribed to such terms in the Series B Warrant Agreement (the “Warrant Agreement”) pursuant to which the Existing Warrants was issued.

(b) “Material Adverse Effect” means a material adverse effect on: (i) the business, condition (financial or otherwise), results of operations, shareholders’ equity, properties or prospects of the Company; (ii) the long-term debt or capital stock of the Company; or (iii) any of the other transactions contemplated by this Agreement.

ARTICLE II

EXERCISE OF EXISTING WARRANTS AND ISSUANCE OF SERIES C WARRANTS

Section 2.1 Exercise of Existing Warrants. Holder hereby agrees, as indicated on the signature page hereto, to exercise its Existing Warrants for a cash exercise payment pursuant to the terms of the Existing Warrants. The number of Warrant Shares (as defined below) purchased and the aggregate exercise price are set forth on the Holder’s signature page hereto. Within one (1) Trading Day of the date hereof, the Holder shall deliver the aggregate cash exercise price for such Existing Warrants to the wire instructions set forth on the Company’s signature page hereto and within one (1) Trading Day of receipt by the Company of such aggregate cash exercise price, the Company shall deliver the Warrant Shares to the Holder’s DTC account via the DWAC system. The exercise of the Existing Warrants shall otherwise be pursuant to, and subject to the terms of, the Existing Warrants. The date of the closing of the exercise of the Existing Warrants and other transactions contemplated hereunder shall be referred to as the “Closing”.

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Section 2.2 Issuance of Series C Warrants. Within 3 Trading Days of the date hereof, the Company shall deliver to the Holder Series C Warrants to purchase up to a number of shares of Common Stock equal to the same number of Warrant Shares issuable pursuant to the exercise of the Existing Warrants. The Series C Warrants shall be immediately exercisable at an exercise price of $6.25 per share, subject to adjustment therein and will expire on March 4, 2020. The Series C Warrants shall otherwise be substantially in the form attached hereto on Exhibit A. The shares of Common Stock underlying the Series C Warrants shall be referred to herein as the “Warrant Shares.”

Section 2.3 Registration Rights. On or prior to 60 days following the date hereof, the Company shall prepare and file with the Securities and Exchange Commission (the “Commission”) a registration statement covering the resale of all of the Warrant Shares underlying the Series C Warrants (“Registrable Securities”) for an offering to be made on a continuous basis pursuant to Rule 415; provided, however, that no Holder shall be required to be named as an “underwriter” without such Holder’s express prior written consent. The Company shall use commercially reasonable efforts to cause a registration statement filed under this Agreement to be declared effective under the Securities Act as promptly as possible after the filing thereof, but in any event no later than 120 days following the date hereof (the “Registration Commencement Date”), and shall use commercially reasonable efforts to keep such registration statement continuously effective under the Securities Act until the date that all Registrable Securities covered by such registration statement (i) have been sold, thereunder or pursuant to Rule 144, or (ii) may be sold without volume or manner-of-sale restrictions pursuant to Rule 144 (assuming cashless exercise) and without the requirement for the Company to be in compliance with the current public information requirement under Rule 144, as determined by the counsel to the Company pursuant to a written opinion letter to such effect, addressed and acceptable to the Company’s transfer agent and the affected Holders. In addition, from and after the Registration Commencement Date, the Company agrees to use its reasonable best efforts to register such shares of Common Stock under the blue sky laws of the states of residence of the exercising Warrant holders to the extent an exemption from such registration is not available. Violations by the Company of this Section 2.3 shall result in cashless exercise of the Series C Warrants in accordance with their terms. In addition, if at any time after the Registration Commencement Date, the Company does not have an effective registration statement covering the resale the Warrant Shares, and Rule 144 is not available for the resale of such Warrant Shares due to the failure of the Company to be currently reporting under the Securities Exchange Act of 1934 (“Public Information Failure”), then the Company shall pay in cash by wire transfer of immediately available funds an amount per month equal to 1% of the aggregate VWAP of the shares into which a New Warrant is converted which are not able to be delivered without legend because of such Public Information Failure to the Holder thereof until such shares are able to be delivered without legend (to be prorated for any periods which are less than one month).

Section 2.4 Subsequent Equity Sales. From the date hereof until the date on which the Company files with the Commission a registration statement covering the resale of all of the Registrable Securities, neither the Company nor any Subsidiary shall issue, enter into any agreement to issue or announce the issuance or proposed issuance of any shares of Common Stock or Common Stock Equivalents.

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Section 2.5 Subsequent Agreements. During such time as the Series C Warrants are unexercised, the Company acknowledges and agrees that it will not enter into any agreement with any holder of an Existing Warrant issued by the Company on November 18, 2014 in connection with such Holder’s rights in such Existing Warrant and granting rights materially more favorable than those set forth in this Agreement, without the prior written consent of the Holders of a majority of the Warrant Shares then exercisable under each Warrant Exercise Agreement with the Company dated on or about the date hereof. For avoidance of doubt, an agreement with the same terms set forth herein when the Company’s stock price is higher than the date hereof would constitute an agreement with rights materially more favorable than those set forth in this Agreement.

Section 2.6 Filing of Form 8-K and Prospectus Supplement. Prior to 9:30 am ET on the date hereof, the Company shall issue a Current Report on Form 8-K, reasonably acceptable to the Holder disclosing the material terms of the transactions contemplated hereby, which shall include this Agreement and the Form of Series C Warrant Agreement as an attachment thereto (the “8-K Filing”); provided however, if this Agreement is executed after 9:30 am ET the 8-K Filing shall be filed prior to 9:30 am ET on the following Trading Day. From and after the issuance of the 8-K Filing, the Company represents to the Holder that it shall not be in possession of any material, nonpublic information received from the Company, any of its Subsidiaries or any of their respective officers, directors, employees or agents, that is not disclosed in the 8-K Filing. In addition, effective upon the filing of the 8-K Filing, the Company acknowledges and agrees that any and all confidentiality or similar obligations under any agreement, whether written or oral, between the Company, any of its Subsidiaries or any of their respective officers, directors, affiliates, employees or agents, on the one hand, and the Holder or any of its affiliates, on the other hand, shall terminate. The Company shall not, and shall cause each of its Subsidiaries and its and each of their respective officers, directors, employees and agents, not to, provide the Holder with any material, nonpublic information regarding the Company or any of its Subsidiaries from and after the date hereof without the express prior written consent of the Holder. To the extent that the Company, any of its Subsidiaries or any of their respective officers, directors, employees or agents, delivers any material, non-public information to the Holder without such Holder’s consent, the Company hereby covenants and agrees that such Holder shall not have any duty of confidentiality with respect to, or a duty not to trade on the basis of, such material, non-public information. In addition, within 1 Trading Day of the date hereof, the Company shall file a prospectus supplement under Rule 424 under the Securities Act to registration statement on Form S-1 (No. 333-196635) (the “Registration Statement”), disclosing the terms of the transactions hereunder.

Section 2.7 Conditions to Holder’s Obligations. The obligations of the Holder hereunder in connection with the Closing are subject to the following conditions being met:

(a) the accuracy in all material respects (or, to the extent representations or warranties are qualified by materiality or Material Adverse Effect, in all respects) on the date of the Closing of the representations and warranties of the Purchasers contained herein (unless as of a specific date therein in which case they shall be accurate as of such date);

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(b) the Registration Statement shall be effective as of the Closing Date for the issuance and resale by the Holder of the Warrant Shares underlying the Existing Warrants;

(c) all obligations, covenants and agreements of the Company required to be performed at or prior to the Closing shall have been performed, including the delivery of a Secretary’s Certificate, attaching the Board of Directors resolutions approving the transactions contemplated hereby;

(d) there shall have been no Material Adverse Effect with respect to the Company since the date hereof; and

(e) from the date hereof to the Closing, trading in the Common Stock shall not have been suspended by the Commission, and, at any time prior to the Closing, trading in securities generally as reported by Bloomberg Financial Markets shall not have been suspended or limited, or minimum prices shall not have been established on securities whose trades are reported by such service, or on any Trading Market, nor shall a banking moratorium have been declared either by the United States or New York State authorities nor shall there have occurred any material outbreak or escalation of hostilities or other national or international calamity of such magnitude in its effect on, or any material adverse change in, any financial market which, in each case, in the reasonable judgment of the Holder, makes it impracticable or inadvisable to consummate the transactions hereunder.

Section 2.8 Opinion of Company Counsel. The Company shall use commercially reasonable good faith efforts to obtain on or prior to March 9, 2015 a legal opinion of the Company’s U.S. corporate counsel typical for similar transactions and in form and substance reasonably acceptable to both U.S. corporate counsel and the Holder.

ARTICLE III

REPRESENTATIONS AND WARRANTIES

Section 3.1 Representations and Warranties of the Company. The Company hereby makes the representations and warranties set forth below to the Holder that as of the date of its execution of this Agreement:

(a) Authorization; Enforcement. The Company has the requisite corporate power and authority to enter into and to consummate the transactions contemplated by this Agreement and otherwise to carry out its obligations hereunder and thereunder. The execution and delivery of this Agreement by the Company and the consummation by it of the transactions contemplated hereby have been duly authorized by all necessary action on the part of such Company and no further action is required by such Company, its board of directors or its stockholders in connection therewith. This Agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof

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will constitute the valid and binding obligation of the Company enforceable against the Company in accordance with its terms except (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

(b) Registration Statement. The Warrant Shares underlying the Existing Warrants are registered for issuance and resale by the Holder on the Registration Statement and the Company knows of no reasons why such registration statement shall not remain available for the issuance and resale of such Warrant Shares for the foreseeable future. The Company shall use commercially reasonable efforts to keep the Registration Statement effective and available for use by the Holder until all Warrant Shares underlying the Existing Warrants are sold by the Holder.

(c) No Conflicts. The execution, delivery and performance of this Agreement by the Company and the consummation by the Company of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Company’s certificate or articles of incorporation, bylaws or other organizational or charter documents, or (ii) conflict with, or constitute a default (or an event that with notice or lapse of time or both would become a default) under, result in the creation of any lien upon any of the properties or assets of the Company, or give to others any rights of termination, amendment, acceleration or cancellation (with or without notice, lapse of time or both) of, any material agreement, credit facility, debt or other material instrument (evidencing Company debt or otherwise) or other material understanding to which the Company is a party or by which any property or asset of the Company is bound or affected, or (iii) conflict with or result in a violation of any law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority to which the Company is subject (including federal and state securities laws and regulations), or by which any property or asset of the Company is bound or affected.

(d) Disclosure. Except with respect to the material terms and conditions of the transactions contemplated by this Agreement, the Company confirms that neither it nor any other Person acting on its behalf has provided any of Holder or their agents or counsel with any information that it believes constitutes or might constitute material, non-public information. The Company understands and confirms that the Holder will rely on the foregoing representation in effecting transactions in securities of the Company. All of the disclosure furnished by or on behalf of the Company to the Holder regarding the Company and its Subsidiaries, their respective businesses and the transactions contemplated hereby, including but not limited to the disclosure set forth in the SEC Reports, is true and correct and does not contain any untrue statement of a material fact or omit to state any material fact necessary in order to make the statements made therein, in light of the circumstances under which they were made, not misleading. As used herein, “SEC Reports” means all reports, schedules, forms, statements and other documents required to be filed by the Company with the Commission pursuant to the

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reporting requirements of the 1934 Act, including all exhibits included therein and financial statements, notes and schedules thereto and documents incorporated by reference therein.

Section 3.2 Representations and Warranties of the Holder. The Holder hereby makes the representations and warranties set forth below to the Company that as of the date of its execution of this Agreement:

(a) Due Authorization. The Holder represents and warrants that (i) the execution and delivery of this Agreement by it and the consummation by it of the transactions contemplated hereby have been duly authorized by all necessary action on its behalf and (ii) this Agreement has been duly executed and delivered by the Holder and constitutes the valid and binding obligation of the Holder, enforceable against it in accordance with its terms.

(b) No Conflicts. The execution, delivery and performance of this Agreement by the Holder and the consummation by the Holder of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Holder’s organizational or charter documents, or (ii) conflict with or result in a violation of any agreement, law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority which would interfere with the ability of the Holder to perform its obligations under this Agreement.

(c) Access to Information. The Holder acknowledges that it has had the opportunity to review this Agreement and the SEC Reports and has been afforded (i) the opportunity to ask such questions as it has deemed necessary of, and to receive answers from, representatives of the Company concerning the terms and conditions of the exercise of the Existing Warrants and issuance of the Series C Warrants and the merits and risks of investing in the Warrant Shares underlying the Existing Warrants; (ii) access to information about the Company and its financial condition, results of operations, business, properties, management and prospects sufficient to enable it to evaluate its investment; and (iii) the opportunity to obtain such additional information that the Company possesses or can acquire without unreasonable effort or expense that is necessary to make an informed investment decision with respect to the investment. The Holder acknowledges and agrees that neither Maxim Group LLC (the “Advisor”) nor any Affiliate of the Advisor has provided the Holder with any information or advice with respect to the Securities nor is such information or advice necessary or desired. Neither the Advisor nor any Affiliate has made or makes any representation as to the Company or the quality of the securities issued and issuable hereunder and the Advisor and any Affiliate may have acquired non-public information with respect to the Company which the Holder agrees need not be provided to it. In connection with the issuance of the securities hereunder to the Holder, neither the Advisor nor any of its Affiliates has acted as a financial advisor or fiduciary to the Holder.

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(d) Holder Status. At the time such Holder was offered the Series C Warrants, it was, and as of the date hereof it is, and on each date on which it exercises any Series C Warrants, it will be either: (i) an “accredited investor” as defined in Rule 501(a)(1), (a)(2), (a)(3), (a)(7) or (a)(8) under the Securities Act or (ii) a “qualified institutional buyer” as defined in Rule 144A(a) under the Securities Act.

ARTICLE IV

MISCELLANEOUS

Section 4.1 Notices. Any and all notices or other communications or deliveries required or permitted to be provided hereunder shall be made in accordance with the provisions of the Warrant Agreement.

Section 4.2 Survival. All warranties and representations (as of the date such warranties and representations were made) made herein or in any certificate or other instrument delivered by it or on its behalf under this Agreement shall be considered to have been relied upon by the parties hereto and shall survive the issuance of the Existing Warrants. This Agreement shall inure to the benefit of and be binding upon the successors and permitted assigns of each of the parties; provided however that no party may assign this Agreement or the obligations and rights of such party hereunder without the prior written consent of the other parties hereto.

Section 4.3 Execution. This Agreement may be executed in two or more counterparts, all of which when taken together shall be considered one and the same agreement and shall become effective when counterparts have been signed by each party and delivered to the other party, it being understood that both parties need not sign the same counterpart. In the event that any signature is delivered by facsimile transmission, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such facsimile signature page were an original thereof.

Section 4.4 Severability. If any provision of this Agreement is held to be invalid or unenforceable in any respect, the validity and enforceability of the remaining terms and provisions of this Agreement shall not in any way be affected or impaired thereby and the parties will attempt to agree upon a valid and enforceable provision that is a reasonable substitute therefor, and upon so agreeing, shall incorporate such substitute provision in this Agreement.

Section 4.5 Governing Law. All questions concerning the construction, validity, enforcement and interpretation of this Agreement shall be determined pursuant to the Governing Law provision of the Warrant Agreement.

Section 4.6 Entire Agreement. The Agreement, together with the exhibits and schedules thereto, contain the entire understanding of the parties with respect to the subject matter hereof and supersede all prior agreements and understandings, oral or written, with respect to such matters, which the parties acknowledge have been merged into such documents, exhibits and schedules.

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Section 4.7 Construction. The headings herein are for convenience only, do not constitute a part of this Agreement and shall not be deemed to limit or affect any of the provisions hereof. The language used in this Agreement will be deemed to be the language chosen by the parties to express their mutual intent, and no rules of strict construction will be applied against any party.

Section 4.8 Termination. This Agreement may be terminated by any Holder, as to the Holder’s obligations hereunder, by written notice to the other parties, if the Closing has not been consummated on or before March 9, 2015, unless such failure shall be due to the failure of Holder to perform or comply with any of the covenants, agreements or conditions hereof to be performed or complied with by it prior to the Closing.

Section 4.9 Fees and Expenses. Except as expressly set forth herein, each party shall pay the fees and expenses of its advisers, counsel, accountants and other experts, if any, and all other expenses incurred by such party incident to the negotiation, preparation, execution, delivery and performance of this Agreement. The Company shall pay all transfer agent fees, stamp taxes and other taxes and duties levied in connection with the delivery of any Series C Warrants or Warrant Shares.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed by their respective authorized signatories as of the date first indicated above.

Wire Instructions:

COMPANY WIRE INSTRUCTIONS

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[PURCHASER SIGNATURE PAGES TO CAPNIA

WARRANT EXERCISE AGREEMENT]

IN WITNESS WHEREOF, the undersigned have caused this Agreement to be duly executed by their respective authorized signatories as of the date first indicated above.

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Exhibit A

Series C Warrant

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