My grandparents also have a cat that is terrified of me, a big, very fat Tonka named Butch. Faile's idea should work... I know that with Butch, if I sit long enough (still enough) in one place, he eventually comes out to investigate. Even then, he is very nervous around me, but it's a start. The main thing has definitely got to be SERIOUS patience. Just try sitting very still very quietly at first, and don't move while he's around. Then, once he starts to get used to that, try reading and let him get accustomed to your voice. Perhaps try leaving treats out for him nearby while you're around to encourage him to try to come out (he probably won't take it out of your hand for a while). Like I say, most of all, just try to be very patient; it might a long time. Let him get used to your presence in the room for a while before you try anything else.