THE ANALYTICAL SOLUTIONS OF EUROPEAN OPTIONS ON SHARES PRICING MODELS

Abstract

The Black-Scholes options formula is the breakthrough in valuating options prices. However, the formula is heavily based on several assumptions that are not realistic in practice. The extensions of the assumptions are needed to make options pricing model more realistic. This paper has reviewed the relaxation of the formula to European options on shares with the focus on its analytical solutions. The assumptions that are relaxed are non-dividends assumption, constant interest rate, constant volatility, and continuous time. Abstract in Bahasa Indonesia : Rumus opsi saham Black-Scholes merupakan terobosan dalam penentuan nilai suatu wahana keuangan derivatif opsi saham. Namun demikian, rumus ini didasari beberapa asumsi yang dalam praktiknya tidak realistis. Pengembangan asumsi tersebut diperlukan agar model penilaian harga opsi saham lebih realistis. Tulisan ini membahas relaksasi asumsi dalam rumus Black-Scholes terhadap opsi Eropa pada saham yang berfokus pada solusi analitis. Relaksasi asumsi yang dibahas merupakan asumsi tanpa dividen, suku bunga konstan, volatilitas tetap, dan waktu yang kontinu. Kata kunci: Opsi, penilaian opsi saham, solusi analitis, rumus Black-Scholes.