Never shortchange yourself - ever. If you have a low current salary, state that you need a significant boost. If the potential employer knows how low yours is, you'll see just what they consider a significant boost then.
That increase will tell you a lot. Are they thinking you're not worth much because of the low salary and give you a small boost? Then they probably won't pay you well no matter what. If they do give you a bit better than you expected of a boost, that means they recognize your talent or indeed want you for the job - a much better outcome.
Consider what your minimum increase is and then when asked, put it on the table. Don't be greedy but be firm; financial firms look for weak negotiators or people that shortchange themselves. You're not worth as much to them if you won't stand up for your needs.
Right. Shortchange the company instead.
OP, considering your virtually nonexistent professional experience, I'd take the job regardless of the salary and focus on learning as much as I can. Ignore the money for a couple years.
Then bump up to a higher payscale, either at the same company or jumping ship to a different one.
I don't mean shortchange the company. I mean don't shortchange yourself.
@OP, If you accept less than you are worth people will continue to offer you exactly that. I don't mean be unreasonable; I mean don't accept the age-old argument "oh, but you'll get experience".
Even when you are starting out, stand up for what you are worth. You won't regret it.
My current job pays abysmally low, but it offered great experience when I didn't have any. And I'm getting more interesting opportunities now because of it.
So now I can afford to be a little less desperate.
I think the fact its in finance is what skews things. I'm very frugal, so I don't want to feel as if I made out like a bandit when in fact I really got something below market rate.
Doesn't mean I won't take something below market rate, but I'd like to have that information when I evaluate an offer.
Finance is a domain with a lot of money. So, if you have domain knowledge and can help the firm make a lot of money, you can make a lot of money too. But if you don't, don't expect a dime more than at another company. In fact, they may pay you less, in return for gaining the domain knowledge, which you can later turn into a lot of money.