<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0203</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2009-09-29</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001163348</issuerCik>
        <issuerName>ALLIED WORLD ASSURANCE CO HOLDINGS LTD</issuerName>
        <issuerTradingSymbol>AWH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001474077</rptOwnerCik>
            <rptOwnerName>Bell David</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>COO,  AWAC</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17301</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Employee Stock Options (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.52</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2004-12-31</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3333</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Employee Stock Options (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>32.70</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2006-01-03</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2015-01-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3333</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1250</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 14,625 Restricted Stock Units which convert into Common Shares upon the vesting of such units on a one-for-one basis.</footnote>
        <footnote id="F2">These securities vested in four equal annual installments with the first installment vesting on the date shown.</footnote>
        <footnote id="F3">The Restricted Stock Units vest in four equal annual installments with the first installment vesting on February 26, 2010.</footnote>
        <footnote id="F4">Grant of Restricted Stock Units for no monetary consideration.  2,500 Restricted Stock Units convert into (i) 1,250 Common Shares of the Company and (ii) cash equal to the market value of 1,250 Common Shares (measured at the date of vesting) upon the vesting of such Restricted Stock Units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David A. Bell</signatureName>
        <signatureDate>2009-10-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
