Of all these 4 words only one would fit.

The financial crisis causes a lot of problems. - Финансовый кризис вызывает много проблем.

But it's even better to find other variants for a better sounding translation. For instance, В результате финансового кризиса возникает много проблем (A lot of problems appear as a result of the financial crisis), or something like that...

in addition to 'cause' the other meanings are these:
причинять - be reason of, result
производить - produce, make
заставлять - make, force
вызывать - cause, be reason of, be origin of