PENURUNAN MODEL BLACK SCHOLES DENGAN PERSAMAAN DIFERENSIAL STOKASTIK UNTUK OPSI TIPE EROPA

Authors

  • Desi Susanti
  • Dodi Devianto

DOI:

https://doi.org/10.25077/jmu.3.1.17-26.2014

Abstract

Opsi tipe Eropa adalah kontrak yang memberikan hak kepada pemilik atau
pemegangnya untuk membeli atau menjual sejumlah aset (saham) suatu perusahaan tertentu dengan harga tertentu (harga pelaksanaan), yang dilaksanakan saat jatuh tempo
saja. Harga opsi saham dapat ditentukan dengan model Black Scholes yang dirumuskan
oleh Fisher Black dan Mayor Scholes pada tahun 1973. Model ini mengasumsikan bahwa
harga saham tidak membayarkan dividen, tidak ada pembayaran pajak, suku bunga bebas resiko, dan opsi yang digunakan bertipe Eropa. Perubahan harga saham yang terjadi
di pasar bergerak secara acak menurut waktu. Perubahan tersebut dapat diasumsikan
mengikuti proses Wiener yang merupakan suatu gerak Brown. Perubahan harga saham
yang mengikuti gerak Brown dapat diformulasikan kedalam suatu persamaan diferensial stokastik, dimana solusinya dapat menentukan model Black Scholes. Perhitungan
harga opsi saham Sony Corporation periode 31 Desember 2012 sampai 31 Desember
2013 deng-an Black Scholes menunjukkan bahwa pada semua harga pelaksanaan yang
dipakai sebaiknya opsi call dibeli karena harga opsi di pasar lebih rendah dibandingkan
yang dihitung dengan Black Scholes, sedangkan untuk opsi put pada harga pelaksanaan
19.00 dolar sebaiknya opsi dijual.

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Published

01-03-2014

Issue

Vol. 3 No. 1 (2014)

Section

Articles

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