The only way to be sure it's safe is to setup an IPSec VPN tunnel to either the broker (not likely) or to something at a known-safe location (e.g., home).
IPSec isn't perfect, either, but it is much harder to listen/intercept.
While your broker instructions would keep someone from transfering out your money, it would not keep them from actually trading with your account should someone be able to hack it - they could just grind it into the ground (highly unlikely, I'm sure, but something to think about).
Before someone says "SSL is secure" ever hear of a man-in-the-middle attack? That neighbor could, for example, have a BlueCoat proxy w/ SSL inspection (the man-in-the-middle part) with a signed certificate and you would not get an alert from your web browser (default setting). You would either need a browser that can alert/refuse a proxied certificate (M-I-T-M) or you'd have to sniff (packet capture) your network traffic to catch it.
How well do you know the neighbor? If you trust him/her and that network, then it's probably acceptable if s/he is using WPA2 to secure the wireless network. If it's just WEP the network is not secure. As far as WPA (as in "WPA1") is not as easy to crack as WEP but it is crackable.
Something else to consider is that in some very poor countries, the wired connections to the ISPs can't be trusted, either. I'm not saying that where you're going is like that - it's just something else to be paranoid about
