I have a MS SQL table that contains stock data with the following columns: Id, Symbol, Date, Open, High, Low, Close.
I would like to self-join the table
What you had is fine. I don't know if translating the sub-query into the join will help. However, you asked for it, so the way to do it might be to join the table to itself once more.
select *
from quotes t1
inner join quotes t2
on t1.symbol = t2.symbol and t1.date > t2.date
left outer join quotes t3
on t2.symbol = t3.symbol and t2.date > t3.date
where t3.date is null