<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>0210 - Disclosure - Derivative Instrument and Hedging Activity</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2010 - 12/31/2010
USD ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>Jan-01-2010_Dec-31-2010</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000105634</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2010-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2010-12-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>USDEPS</UnitID><UnitType>Divide</UnitType><NumeratorMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></NumeratorMeasure><DenominatorMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="12 Months Ended" /><Label Id="2" Label="Dec. 31, 2010" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_DerivativeInstrumentsAndHedgesAbstract</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Derivative Instrument and Hedging Activity [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 10 - us-gaap:DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock--&gt;
   &lt;div style="margin-left: 0%"&gt;
   &lt;div style="margin-top: 18pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;table width="100%" border="0" cellpadding="0" cellspacing="0" style="font-size: 10pt; font-family: Arial, Helvetica; color: #000000; background: transparent; text-align: left"&gt;
   &lt;tr&gt;
       &lt;td width="9%"&gt;&lt;/td&gt;
       &lt;td width="91%"&gt;&lt;/td&gt;
   &lt;/tr&gt;
   &lt;tr valign="top"&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;NOTE&amp;#160;10&amp;#8212;&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
       &lt;td&gt;
       &lt;b&gt;&lt;font style="font-family: 'Times New Roman', Times"&gt;DERIVATIVE
       INSTRUMENT AND HEDGING ACTIVITY&lt;/font&gt;&lt;/b&gt;
   &lt;/td&gt;
   &lt;/tr&gt;
   &lt;/table&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       On January&amp;#160;27, 2009, we entered into an interest rate swap
       agreement (the &amp;#8220;Swap Agreement&amp;#8221;), which hedged the
       interest rate risk on our variable rate debt. The Swap Agreement
       matured in October 2010 and was used to manage the variable
       interest rate of our borrowings and related overall cost of
       borrowing. We mitigated the risk of counterparty nonperformance
       by choosing as our counterparty a major reputable financial
       institution with an investment grade credit rating.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       The derivative was recognized as either an asset or liability on
       our Consolidated Balance Sheets with measurement at fair value,
       and changes in the fair value of the derivative instrument were
       reported in either net income, included as part of interest
       expense, or other comprehensive income, depending on the
       designated use of the derivative and whether or not it met the
       criteria for hedge accounting. The fair value of this instrument
       reflected the net amount required to settle the position. The
       accounting for gains and losses associated with changes in fair
       value of the derivative and the related effects on the
       consolidated financial statements was subject to their hedge
       designation and whether they met effectiveness standards.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       We paid a fixed rate on the Swap Agreement of 2.225% and
       received a floating rate of 30&amp;#160;day LIBOR on the notional
       amount. A portion of the interest rate swap had been designated
       as an effective cash flow hedge, whereby changes in the cash
       flows from the swap perfectly offset the changes in the cash
       flows associated with the floating rate of interest. See
       Note&amp;#160;9&amp;#8212;Debt of the notes to consolidated financial
       statements for additional information. The fair value of the
       interest rate swap at December&amp;#160;31, 2009 was a net liability
       of $1.2&amp;#160;million. This liability reflected the interest rate
       swap&amp;#8217;s termination value as the credit value adjustment for
       counterparty nonperformance was immaterial. We had no obligation
       to post any collateral related to this derivative. The fair
       value of the interest swap was based upon the valuation
       technique known as the market standard methodology of netting
       the discounted future fixed cash flows and the discounted
       expected variable cash flows. The variable cash flows were based
       on an expectation of future interest rates (forward curves)
       derived from observable interest rate curves. In addition, we
       had incorporated a credit valuation adjustment into our
       calculation of fair value of the interest rate swap. This
       adjustment recognized both our nonperformance risk and
   the counterparty&amp;#8217;s nonperformance risk. The net liability
       was included in &amp;#8220;Other accrued expenses and
       liabilities&amp;#8221; on our Consolidated Balance Sheet. Accumulated
       other comprehensive loss at December&amp;#160;31, 2009 included the
       accumulated loss, net of income taxes, on the cash flow hedge,
       of $0.6&amp;#160;million.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       On December&amp;#160;1, 2009, we de-designated $45.5&amp;#160;million of
       the interest rate swap as it was determined that it was no
       longer probable that the future estimated cash flows were going
       to occur as originally estimated. We discontinued the
       application of hedge accounting associated with this portion of
       the interest rate swap, and $0.2&amp;#160;million and
       $0.3&amp;#160;million was expensed as part of interest expense, and
       removed from Accumulated other comprehensive loss, for the years
       ended December&amp;#160;31, 2010 and 2009, respectively.
   &lt;/div&gt;
   &lt;div style="margin-top: 6pt; font-size: 1pt"&gt;&amp;#160;
   &lt;/div&gt;
   &lt;div align="left" style="margin-left: 0%; margin-right: 0%; text-indent: 3%; font-size: 10pt; font-family: 'Times New Roman', Times; color: #000000; background: transparent"&gt;
       As of December&amp;#160;31, 2009, the fair value of our derivative
       was $1.2&amp;#160;million and was in a net liability position
       reflecting the interest rate swap&amp;#8217;s termination value as
       the credit value adjustment for counterparty nonperformance was
       immaterial. As of December&amp;#160;31, 2010, we have no derivatives
       &lt;font style="white-space: nowrap"&gt;and/or&lt;/font&gt;
       hedging instruments outstanding.
   &lt;/div&gt;
   &lt;/div&gt;
</NonNumbericText><NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>This element can be used to disclose the entity's entire derivative instruments and hedging activities disclosure as a single block of text. Describes an entity's risk management strategies, derivatives in hedging activities and non-hedging derivative instruments, the assets, obligations, liabilities, revenues and expenses arising there from, and the amounts of and methodologies and assumptions used in determining the amounts of such items.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 133
 -Paragraph 45

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 133
 -Paragraph 44

</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>DERIVATIVE INSTRUMENT AND HEDGING ACTIVITY</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Derivative Instrument and Hedging Activity</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
