Consider a Black&Scholes Market where a risky asset evolves according to: $$\frac{dS_t}{S_t}=\mu dt+\sigma dB_t$$ $$S_o=s$$ Riskless asset is associated with risk free rate r. I want to represent the value of the payoff given only by the riskless asset using the B&S formula.
Is it correct to simply use the B&S formula by eliminating the underlying part $S_0$ to obtain the payoff of the riskless assets? $$P_o=S_0 \phi (d1)-Ke^{-rT} \phi (d2) $$ $ P_o=S_0 \phi (d1)-Ke^{-rT} \phi (d2) $ (Price of a call) $ P_o=-Ke^{-rT} \phi (d2) $ ( Price of the riskless asset)