Abstract
Option are contracts that give the right to sell and buy the asset at a price and a certain period of time. In addition investors use option as a means of hedge against asset owned. Many methods are used to determine the price of option, one of them by using the Black-Scholes equation. But its use these in the assumption that the value for the constant volatility. On market assumption are not appropriates, so many researchers proposed using a volatility calculation option that is non-constant Black-Scholes equation modelled using the volatility is not constant in the range so as to produce a non-linear equation of Black-Scholes. In addition to determine the value of hedge ratio. On completions of this study, for the numerical solution of non-linear Black-Scholes equation using method of explicit finite difference scheme. Option use in research us a stock YAHOO!inc. as the underlying asset. The result showed that the price of the option is calculated using non-linear Black-Scholes equation price close on the market. Therefore, it can produce hedge ration for a risk-free portfolio containing of the option and stock.
Highlights
Option are contracts that give the right to sell and buy the asset at a price and a certain period of time
Many methods are used to determine the price of option
In addition to determine the value of hedge ratio
Summary
Perkembangan investasi ditunjukan dengan munculnya berbagai macam alternatif instrumen investasi salah satunya adalah opsi. Opsi merupakan kontrak yang memberikan hak untuk membeli atau menjual aset pada harga dan jangka waktu tertentu. Opsi kerap digunakan oleh investor sebagai sarana untuk melakukan lindung nilai (hedging) terhadap aset yang dimiliki. Terdapat berbagai cara yang dapat dilakukan dalam menghitung harga opsi, salah satu cara yang sering digunakan dalam dunia keuangan adalah model Black-Scholes. Dengan asumsi nilai volatilitas yang konstan, penerapan persamaan Black-Scholes ini dianggap belum sesuai dengan keadaan nyata dalam pasar keuangan. Sehingga model diturunkan menggunakan persamaan diferensial stokastik yang mengasumsikan diketahui adanya rentang dalam nilai volatilitas. Model tersebut mengubah asumsi bahwa volatilitas yang dianggap konstan diubah menjadi tidak konstan sehingga dapat ditentukan nilai opsinya. Selanjutnya akan ditentukan nilai hedge ratio menggunakan model Non-Linear Black-Scholes
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