Abstract
The purpose of this research is to compare the selling price of down and out barrier option when the prices are simulated by the Antithetic Variate Monte Carlo and the standar Monte Carlo. Barrier options are path dependent options and the payoff depend on whether the underlying asset price touched the barrier or not during the life of the option. In this research, we conducted simulations against the closing price of the shares of PT Adhi Karya using Standard Monte Carlo simulation and the Monte Carlo-Antithetic Variate simulation. After the simulation, we obtained that the option prices using Antithetic Variate produces a cheaper price than the standar one. We also found that the analytic solution has a smaller error on its confidence interval compare to the Monte Carlo Standar.
Highlights
The purpose of this research is to compare the selling price of down and out barrier option when the prices are simulated by the Antithetic Variate Monte Carlo and the standar Monte Carlo
We also found that the analytic solution has a smaller error on its confidence interval compare to the Monte Carlo Standar
Pricing Barrier Options using Monte Carlo Methods, Uppsala: Department of Mathtematics Uppsala University
Summary
Instrumen yang diperdagangkan dan banyak diminati adalah opsi. Opsi merupakan perjanjian atau kontrak antara penjual opsi (seller atau writer) dengan pembeli opsi (buyer), di mana penjual opsi menjamin adanya hak tetapi bukan suatu kewajiban dari pembeli opsi, untuk membeli atau menjual suatu aset tertentu pada waktu dan harga yang telah ditetapkan, apabila saat waktu jatuh tempo (expiration date) pemegang opsi tidak menggunakan haknya, maka hak tersebut akan hilang dengan sendirinya (Tandelilin, 2010). Salah satu metode yang digunakan dalam perhitungan harga opsi adalah metode Monte Carlo. Berdasarkan penelitian yang telah dilakukan penulis tertarik untuk mengkaji lebih dalam teknik pengurangan varians khususnya antithetic variateyang diterapkan dalam menentukan harga jual opsi barrier tipe Eropa. Anthitetic variate merupakan salah satu bagian dari teknik pengurangan varian yang ada pada simulasi Monte Carlo.Ide dasar teknik ini yaitu melibatkan perhitungan dua buah nilai opsi yaitu dan Perhitungan harga opsi menggunakan teknik Antithetic variate mengikuti Gerak. Simulasi Monte Carlo-Antithetic Variate dalam menentukan harga opsi dapat diuraikan sebagai berikut: 1. Menetapkan variabel-variabel yang diperlukan dalam perhitungan yaitu yaitu nilai saham awal ( ), waktu jatuh tempo (T), harga kesepakatan (K), suku bunga bebas risiko (r), nilai barrier (H), standar deviasi (σ) dan dividen = 0
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