Pembahasan Ujian PAI: F10 – No. 05 – November 2025

Standar deviasi imbal hasil saham: \(\sigma = 40\%\);

Tingkat suku bunga bebas risiko: \(r = 10\%\);

Dividen:

Strike price: \(K = 70\)

Waktu jatuh tempo: \(T = 145\) hari

$$\begin{aligned}
C &= S_{0}\,N\left(d_{1}\right) – Ke^{-rT}N\left(d_{2}\right) \\
P &= Ke^{-rT}N\left(-d_{2}\right) – S_{0}\,N\left(-d_{1}\right) \\
d_{1} &= \frac{\ln\left(\frac{S_{0}}{K}\right) + \left(r + \frac{1}{2}\sigma^{2}\right)T}{\sigma\sqrt{T}} \\
d_{2} &= d_{1} – \sigma\sqrt{T}
\end{aligned}$$

$$\begin{aligned}
S_{0}’ &= S_{0} – PV(\text{dividen}) \\
&= S_{0} – \left(D_{1}e^{-rt_{1}} + D_{2}e^{-rt_{2}}\right) \\
&= 72 – \left(2e^{-0,1 \times \frac{40}{365}} + 2{,}5e^{-0,1 \times \frac{130}{365}}\right) \\
&= 72 – \left(1{,}97819 + 2{,}41254\right) \\
&= 67{,}60927
\end{aligned}$$

Menghitung harga opsi beli:

$$\begin{aligned}
d_{1} &= \frac{\ln\left(\frac{S_{0}’}{K}\right) + \left(r + \frac{1}{2}\sigma^{2}\right)T}{\sigma\sqrt{T}} \\
&= \frac{\ln\left(\frac{67{,}60927}{70}\right) + \left(10\% + \frac{1}{2}(40\%)^{2}\right)\frac{145}{365}}{40\%\sqrt{\frac{145}{365}}} \\
&= 0{,}14579 \\[6pt] d_{2} &= d_{1} – \sigma\sqrt{T} \\
&= 0{,}14579 – 40\%\sqrt{\frac{145}{365}} \\
&= -0{,}10632
\end{aligned}$$

$$\begin{aligned}
C &= S_{0}’\,N\left(d_{1}\right) – Ke^{-rT}N\left(d_{2}\right) \\
&= 67{,}60927\,N(0{,}14579) – 70\,e^{-10\% \times \frac{145}{365}}\,N(-0{,}10632) \\
&= 67{,}60927\,(0{,}55796) – 67{,}28688\,(0{,}45766) \\
&= 37{,}72317 – 30{,}78879 \\
&= 6{,}93438 \approx 6{,}93
\end{aligned}$$

Dengan demikian, harga saat ini dari opsi beli (call option) tipe Eropa atas saham PT Huntrix sebesar $6,93.