If you are using your parent's address to open a US account, then you are stating that is your actual residence. Because of credit checks and IRS cross checks, even if you can do this initially, (the bank sets you up) after a few years, it will cause problems. You also need to show your identification to that address, I believe... (?)
When I moved back to Canada from the USA, it only took a couple of years for the bank to notify me that I was no longer resident, and then to freeze my trading account (because they do not report for trading accounts for non-residents). I did not update my residential address to my Canadian one, only redirected mail, and then updated the mailing address. I am not sure what the trigger was - my DL expiring in the USA, my mailing address being CDN for so long, or the basic Equifax credit report showing an updated address not in the USA (they collect this over time).
The biggest problem is if one government decides that you are US resident, and the other decides CDN resident and it causes an IRS tax tangle. And they use the address you gave your bank, that you called your residential address, as your actual residence, as support for their arguement.
A smaller problem is remembering all of your "last known addresses" for future credit , job, security, passport, etc applications. For a security clearance for work, I have had to enter in all my addresses for the past 10 years and boy am I glad that I always set it up truthfully, because after 7 years, it is very very hard to remember all the actual addresses, let alone which ones were on file versus where your "temporarily" lived... I had 9 actual addresses in 10 years because of job transfers and needing to switch rentals.
The good news - as a Canadian resident, you should be able to open chequing and savings accounts in the USA. Snow birds do this all the time. Some banks will file the paperwork (securities) for non-residents, and you can also open up trading accounts with those, but you need to call around to find out which ones do that.
So, just be above board and do that. - choose the bank and open your accounts.