Show that V $($r$,$ t; T $)=$ Z$($r$,$ t; T $)$E$$

f $[$gT $],$ where V is the price of the security, Z is a zero$-$

coupon bond used as the numeraire, gT is the payoff of the security at maturity T and E$$

f

is the expectation under the forward risk neutral probability measure. Hint: start with the

relationship between V and $$V $.$ Explain all assumptions and equations involved.

$9$