Pembahasan Ujian PAI: A40 – No. 30 – Mei 2026

• Harga saham saat ini: \(S_{0} = 40\)
• Strike price: \(K = 45\)
• Waktu jatuh tempo: \(T = \frac{4}{12} = \frac{1}{3}\) tahun
• Tingkat bunga bebas risiko: \(r = 4{,}75\% = 0{,}0475\)
• Varians imbal hasil saham: \(\sigma^{2} = 0{,}25\)
• Volatilitas: \(\sigma = \sqrt{0{,}25} = 0{,}5\) atau \(50\%\)

$$C = S_{0}\,N\left(d_{1}\right) – K e^{-rT} N\left(d_{2}\right)$$

dengan:

$$\begin{aligned}
d_{1} &= \frac{\ln\left(S_{0}/K\right) + \left(r + \sigma^{2}/2\right)T}{\sigma\sqrt{T}} \\
d_{2} &= d_{1} – \sigma\sqrt{T}
\end{aligned}$$

Keterangan: \(N(d)\) merupakan fungsi distribusi kumulatif normal standar.

$$\begin{aligned}
d_{1} &= \frac{\ln\left(40/45\right) + \left(0{,}0475 + 0{,}25/2\right)\left(\tfrac{1}{3}\right)}{0{,}288675} \\
&= \frac{-0{,}117783 + 0{,}057500}{0{,}288675} \\
&= \frac{-0{,}060283}{0{,}288675} = -0{,}2088
\end{aligned}$$

2. Hitung nilai (\(d_{2}\)).

$$\begin{aligned}
d_{2} &= d_{1} – 0,5\sqrt{1/3} \\
d_{2} & \approx – 0,2975
\end{aligned}$$

3. Tentukan probabilitas kumulatif normal standar.
Berdasarkan tabel distribusi normal standar:

$$\begin{aligned}
N\left(d_{1}\right) \approx 0{,}4173 \\
N\left(d_{2}\right) \approx 0{,}3095
\end{aligned}$$

4. Hitung harga Call Option.

$$\begin{aligned}
C &= 40\left(0{,}4173\right) – 44{,}2931\left(0{,}3095\right) \\
&= 16{,}692 – 13{,}709 \\
&= 2{,}98 \approx 3{,}0
\end{aligned}$$

Jadi, harga opsi beli (call option) sebesar 3,0.