<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>0012 - Disclosure - COMMON STOCK OPTIONS</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>From2013-01-01to2013-06-30</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001402785</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>fpmi_NotesToFinancialStatementsAbstract</ElementName><ElementPrefix>fpmi_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Notes to Financial Statements</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>fpmi_CommonStockOptionsTextBlock</ElementName><ElementPrefix>fpmi_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="From2013-01-01to2013-06-30" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;On February 11, 2011, the Company adopted
its 2011 Equity Incentive Plan (the &amp;#147;Plan&amp;#148;) under which 6,475,750 shares of common stock were reserved for issuance
under options or other equity interests as set forth in the Plan. Under the Plan, options are available for issuance to employees,
officers, directors, consultants and advisors. The Plan provides that the Board of Directors will determine the exercise price
and vesting terms of each option on the date of grant. Options granted under the Plan generally expire ten years from the date
of grant.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;Under the Plan, the Company has issued
161,250 shares of fully paid and non-assessable restricted common stock to a director of the Company.&amp;#160;&amp;#160;These shares of
restricted stock are subject to the terms of the Plan and are unvested and outstanding as of June 30, 2013.&amp;#160;&amp;#160;The shares
shall vest upon the earlier of (i) the occurrence of a Change of Control, as defined in the Plan, (ii) the successful completion
of a Phase II clinical trial for any of the Company&amp;#146;s products, or (iii) the determination by the Board of Directors to provide
for immediate vesting.&amp;#160;&amp;#160;The weighted average grant-date fair value is $0.83 per share.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;The following is a summary of all common
stock option activity for the quarter ended June 30, 2013:&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0"&gt;&amp;#160;&lt;/p&gt;

&lt;table cellspacing="0" cellpadding="0" style="width: 100%; font: 10pt Calibri, Helvetica, Sans-Serif; border-collapse: collapse"&gt;
&lt;tr style="vertical-align: bottom"&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td colspan="2" style="border-bottom: black 1pt solid"&gt;
        &lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: center"&gt;&lt;b&gt;Shares Under&lt;/b&gt;&lt;/p&gt;
        &lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: center"&gt;&lt;b&gt;Options Outstanding&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td colspan="2" style="border-bottom: black 1pt solid"&gt;
        &lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: center"&gt;&lt;b&gt;Weighted Average&lt;/b&gt;&lt;/p&gt;
        &lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: center"&gt;&lt;b&gt;Exercise Price&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: #CCEEFF"&gt;
    &lt;td style="width: 70%; text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;Outstanding at December 31, 2012&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 12%; text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;4,035,428&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 12%; text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;0.66&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: white"&gt;
    &lt;td style="text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;&amp;#160;&amp;#160;&amp;#160;Options granted&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;515,000&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;0.83&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: #CCEEFF"&gt;
    &lt;td style="text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;&amp;#160;&amp;#160;&amp;#160;Options forfeited&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;-&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;-&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: white"&gt;
    &lt;td style="text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;&amp;#160;&amp;#160;&amp;#160;Options exercised&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="border-bottom: black 1pt solid; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="border-bottom: black 1pt solid; text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;-&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="border-bottom: black 1pt solid; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="border-bottom: black 1pt solid; text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;-&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: #CCEEFF"&gt;
    &lt;td style="text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;Outstanding at June 30, 2013&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="border-bottom: black 2.25pt double; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="border-bottom: black 2.25pt double; text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;4,550,428&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="border-bottom: black 2.25pt double; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="border-bottom: black 2.25pt double; text-align: right; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;0.68&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;table cellspacing="0" cellpadding="0" style="width: 100%; font: 10pt Calibri, Helvetica, Sans-Serif; border-collapse: collapse"&gt;
&lt;tr style="vertical-align: bottom"&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td colspan="2" style="border-bottom: black 1pt solid; text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;&lt;b&gt;Options Exercisable&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td colspan="2" style="border-bottom: black 1pt solid"&gt;
        &lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: center"&gt;&lt;b&gt;Weighted Average Exercise&lt;/b&gt;&lt;/p&gt;
        &lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: center"&gt;&lt;b&gt;Price per Share&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: #CCEEFF"&gt;
    &lt;td style="width: 70%; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;Exercisable at December 31, 2012&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 12%; text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;2,294,053&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 12%; text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;0.66&lt;/font&gt;&lt;/td&gt;
    &lt;td style="width: 1%; line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="vertical-align: bottom; background-color: white"&gt;
    &lt;td style="line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;Exercisable at June 30, 2013&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;2,594,053&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;$&lt;/font&gt;&lt;/td&gt;
    &lt;td style="text-align: center; line-height: 115%"&gt;&lt;font style="font: 10pt Times New Roman, Times, Serif; color: black"&gt;0.68&lt;/font&gt;&lt;/td&gt;
    &lt;td style="line-height: 115%"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;The weighted average fair value of options
granted during the six months ended June 30, 2013 was $0.49.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;As of June 30, 2013, the weighted average
remaining contractual term for exercisable and outstanding options is 5.97 and 7.04 years, respectively.&amp;#160;&amp;#160;The aggregate
intrinsic value of all of the Company&amp;#146;s exercisable and outstanding options is approximately $431,000 and $584,000, respectively.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;As of June 30, 2013, there was approximately
$902,000 of unrecognized compensation cost related to non-vested options. The unrecognized compensation expense is estimated to
be recognized over a period of 1.55 years at June 30, 2013.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify"&gt;The Company used the Black-Scholes option
pricing model to value the all option grants (see Note 1, Summary of Significant Accounting Policies, &amp;#147;Accounting for Share
Based Payments&amp;#148;).&lt;/p&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>Custom Element</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Note 7. COMMON STOCK OPTIONS</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>COMMON STOCK OPTIONS</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://flouropharmamedical.com/role/CommonStockOptions</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
