<?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>2114100 - Disclosure - Independent Directors' Stock Option</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>1</Level><ElementName>us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</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>Disclosure of Compensation Related Costs, Share-based Payments [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</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><PreferredLabelRole>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;padding-top:12px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;INDEPENDENT DIRECTORS&amp;#8217; STOCK OPTION PLAN&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:12px;text-indent:24px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The Company has a stock option plan, the Independent Director&amp;#8217;s Stock Option Plan (the &amp;#8220;IDSOP&amp;#8221;), which authorizes the grant of non-qualified stock options to the Company&amp;#8217;s independent directors, subject to the discretion of the board of directors and the applicable limitations of the IDSOP. The term of the IDSOP is &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;ten&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; years, at which time any outstanding options will be forfeited. The exercise price for the options granted under the IDSOP was &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$9.15&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; per share for 2005 and 2006, and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$9.10&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; per share for 2007, 2008 and 2009. The Company does not intend to continue to grant options under the IDSOP; however, the exercise price for any future options granted under the IDSOP will be at least &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;100%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the fair market value of the Company&amp;#8217;s common stock as of the date the option is granted. As of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company had granted options to purchase &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;50,000&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; shares under the IDSOP and options to purchase &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;45,000&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; shares at a weighted average exercise price of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;$9.12&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; per share remained outstanding with a weighted average contractual remaining life of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;four&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; years. &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;No&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; shares were granted or exercised pursuant to the IDSOP for the &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;three and six&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; months ended &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;. A total of &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;1,000,000&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; shares have been authorized and reserved for issuance under the IDSOP.&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;padding-top:12px;text-indent:24px;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;During the &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;three and six&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; months ended &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;June&amp;#160;30, 2013&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; and &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;2012&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;, the Company did not record any stock-based compensation charges, as all stock-based compensation charges related to unvested stock-based compensation awards granted under the IDSOP had previously been recognized. Stock-based compensation expense is based on awards ultimately expected to vest and reduced for estimated forfeitures. Forfeitures are estimated at the time of grant and revised, if necessary, in subsequent periods if actual forfeitures differ from those estimates. 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