From what I understand, your top-most preferred career is in the Securities/FX industry. Unfortunately, you've not managed to obtain a job there despite multiple applications. Nevertheless, although you're still ultimately interested in the Securities/FX industry, you don't mind trying out other job functions in a bank as long as they are decently good.
Current Status: Recent Graduate in
NUS Economics; Have a contract offer at the IT department in a bank.
I don't like to discourage people, but like the other posters, my opinion is that it'll be a tough challenge to get into your preferred job. The reason being: (1) You're a graduate, and thus will not fit into the "undergraduate" criteria for internships in most companies; (2) The securities/fx industry is competitive to get into; (3) The securities/fx industry is getting even tougher every year; (4) Qualifications - I'm not sure of your class of honours and relevant internships.
If you would still like to try, your best bet would be to reach out for connections/people:
1) School: Your Alma Mater's career services and Alumni
2) Personal contacts: Family, Friends, Relatives, etc.
3) Publicly-available information: Apply/network/call/etc to all available Securities/FX jobs in all companies, whether they are in banks, boutiques or family offices.
Doing the above can be very time-consuming and it doesn't guarantee that you'll get a job in the end. However, you'll never know if you never try. One thing to note is that life will not be all rainbows and sunshine even if you manage to get into one in the end. The industry is tough and will be even tougher in the years ahead. Don't think too much about compensation/etc; it may not be as attractive as what you may think it is to be. Job may be quite volatile too.
Anyway, I would think that Tech isn't too bad these days as their roles are changing. However, this would depend on what you actually do within the bank (e.g. pioneering the bank's transformation towards digital platforms, or, just solving technical issues?).