Suppose that the price of a zero-coupon bond maturing at time $T$ follows the process
$$
d P(t, T)=\mu_P P(t, T) d t+\sigma_P P(t, T) d z
$$
and the price of a derivative dependent on the bond follows the process
$$
d f=\mu_f f d t+\sigma_f f d z
$$
Assume only one source of uncertainty and that $f$ provides no income.
(a) What is the forward price $F$ of $f$ for a contract maturing at time $T$ ?
(b) What is the process followed by $F$ in a world defined by the numeraire $P(t, T)$ ?
(c) What is the process followed by $F$ in the traditional risk-neutral world?
(d) What is the process followed by $f$ in a world defined by a numeraire equal to a bond maturing at time $T^*$, where $T^* \neq T$ ? Assume that $\sigma_P^*$ is the volatility of this bond.