"
is the correct way, the third of your tests:
<option value=""asd">test</option>
You can see this working below, or on jsFiddle.
alert($("option")[0].value);
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<select>
<option value=""asd">Test</option>
</select>
Alternatively, you can delimit the attribute value with single quotes:
<option value=""asd">test</option>