Hi, i have several questions when i implement the BGM model, I have seen several time the formula (for exemple in the book of Mercurio & Brigo ), it likes
F(T_i;T_k, T_k+1)=F(T_i-1;T_k, T_k+1)*exp(...(v(T_i-1)...)

My questions are:
1)If I want to know the libor
F(T_i;T_i, T_i+1), F(T_i;T_i+1, T_i+2)...
Should I compute all the libor before the time: e.g.
F(T_i-1; T_i, T_i+1), F(T_i-1, T_i+1, T_i+2)...
F(T_i-2; T_i, T_i+1), F(T_i-2, T_i+1, T_i+2)...
...
2)If the answer of 1) is yes, the input should contain the vol of libor at initial time 0 (v_i(0)) because of
F(1;1,2)=F(0;1,2)*exp(..v(0)..), no?

In fact, I have the results of calibration to swaption with the BGM model, I don't know if they contain also some v(0)

Many thanks for the answer

jo