PENENTUAN HARGA OPSI DAN NILAI HEDGE MENGGUNAKAN PERSAMAAN NON-LINEAR BLACK-SCHOLES

  • PUTU AYU DENI Faculty of Mathematics and Natural Sciences, Udayana University
  • KOMANG DHARMAWAN Faculty of Mathematics and Natural Sciences, Udayana University
  • G. K. GANDHIADI Faculty of Mathematics and Natural Sciences, Udayana University

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.

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Author Biographies

PUTU AYU DENI, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
KOMANG DHARMAWAN, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
G. K. GANDHIADI, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
Published
2016-01-30
How to Cite
DENI, PUTU AYU; DHARMAWAN, KOMANG; GANDHIADI, G. K.. PENENTUAN HARGA OPSI DAN NILAI HEDGE MENGGUNAKAN PERSAMAAN NON-LINEAR BLACK-SCHOLES. E-Jurnal Matematika, [S.l.], v. 5, n. 1, p. 27-31, jan. 2016. ISSN 2303-1751. Available at: <https://ojs.unud.ac.id/index.php/mtk/article/view/18718>. Date accessed: 25 june 2022. doi: https://doi.org/10.24843/MTK.2016.v05.i01.p117.
Section
Articles

Keywords

Black-Scholes; Implied Volatility; non-linear Black-Scholes; hedge ration; finite difference methods; explicit scheme

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