<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="../4_X02.xsl"?><ownershipDocument>    <schemaVersion>X0303</schemaVersion>    <documentType>4</documentType>    <periodOfReport>2009-06-29</periodOfReport>    <notSubjectToSection16>0</notSubjectToSection16>    <issuer>        <issuerCik>0001163348</issuerCik>        <issuerName>ALLIED WORLD ASSURANCE CO HOLDINGS LTD</issuerName>        <issuerTradingSymbol>AWH</issuerTradingSymbol>    </issuer>    <reportingOwner>        <reportingOwnerId>            <rptOwnerCik>0001368325</rptOwnerCik>            <rptOwnerName>Redmond John T</rptOwnerName>        </reportingOwnerId>        <reportingOwnerAddress>            <rptOwnerStreet1>ALLIED WORLD ASSURANCE CO HOLDINGS, LTD</rptOwnerStreet1>            <rptOwnerStreet2>27 RICHMOND ROAD</rptOwnerStreet2>            <rptOwnerCity>PEMBROKE</rptOwnerCity>            <rptOwnerState>D0</rptOwnerState>            <rptOwnerZipCode>HM 08</rptOwnerZipCode>            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>        </reportingOwnerAddress>        <reportingOwnerRelationship>            <isDirector>0</isDirector>            <isOfficer>1</isOfficer>            <isTenPercentOwner>0</isTenPercentOwner>            <isOther>0</isOther>            <officerTitle>Pres, AWAC (Eur) &amp; AWAC (Rein)</officerTitle>        </reportingOwnerRelationship>    </reportingOwner>    <nonDerivativeTable>        <nonDerivativeTransaction>            <securityTitle>                <value>Common Shares</value>            </securityTitle>            <transactionDate>                <value>2009-06-29</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>M</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>1667</value>                </transactionShares>                <transactionPricePerShare>                    <value>23.61</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>A</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>37155</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>        <nonDerivativeTransaction>            <securityTitle>                <value>Common Shares</value>            </securityTitle>            <transactionDate>                <value>2009-06-29</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>S</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>                <footnoteId id="F1"/>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>1667</value>                </transactionShares>                <transactionPricePerShare>                    <value>41.00</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>35488</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>    </nonDerivativeTable>    <derivativeTable>        <derivativeTransaction>            <securityTitle>                <value>Employee Stock Options (right to buy)</value>            </securityTitle>            <conversionOrExercisePrice>                <value>23.61</value>            </conversionOrExercisePrice>            <transactionDate>                <value>2009-06-29</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>M</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>1667</value>                </transactionShares>                <transactionPricePerShare>                    <value>0.00</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <exerciseDate>                <value>2004-01-02</value>                <footnoteId id="F2"/>            </exerciseDate>            <expirationDate>                <value>2013-01-02</value>            </expirationDate>            <underlyingSecurity>                <underlyingSecurityTitle>                    <value>Common Shares</value>                </underlyingSecurityTitle>                <underlyingSecurityShares>                    <value>1667</value>                </underlyingSecurityShares>            </underlyingSecurity>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>0</value>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </derivativeTransaction>    </derivativeTable>    <footnotes>        <footnote id="F1">The exercise of Employee Stock Options and sale of Common Shares reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person on February 27, 2009.</footnote>        <footnote id="F2">These securities vested in four equal annual installments with the first installment vesting on the date shown.</footnote>    </footnotes>    <remarks></remarks>    <ownerSignature>        <signatureName>/s/ Wesley D. Dupont, by Power of Attorney</signatureName>        <signatureDate>2009-06-30</signatureDate>    </ownerSignature></ownershipDocument>