What are some good topics for a project on banking and finance?

There are countless topics to choose from for your project.

Here is a list of topics that I personally find very interesting and relevant to our globalized society:

Corporate governance: given the financial crisis of 2008, what measures should be taken in order to limit the power of financial institutions?

You could elaborate on eliminating the agent-principal problem with brokers and investors. A great movie that emphasizes this topic is "Inside Job"--it's a classic.

Corporate responsibility: how can companies invest in a socially responsible manner?

You could elaborate on impact investing and green investing, which are two hot topics in the investment field.

Globalized markets: given rapid globalization, to what extent are markets becoming more efficient?

You could elaborate on the efficient market hypothesis and explain how information is becoming more accessible.

I hope that this helps!