Analisis Lanjut Metode Beda Hingga Eksplisit Untuk Menentukan Harga Opsi

  • Wahyudi Sastro Universitas Muhammadiyah Ponorogo
DOI: https://doi.org/10.52166/ujmc.v5i01.1302

Abstract

Abstract. Explicit finite difference method is used to approximate a partial differential equation that is applied to determine the option pricing. The results of this study note that the calculation of option pricing using explicit finite difference method is negative when partition N ≥ 25 with a value of -2.21. Thus, the results of the calculation of option pricing are not convergent and away from the results of analyzing the option pricirng (Black-Scholes) solution. This is because one of the three probabilities Bj = 1- σ2j2Δt  is negative, namely (-0.12) when j ≥ 12 with S ≥ 16.25  (in units). So this explicit finite difference method cannot be used to determine the option pricing.

Keywords: Option Pricing, Explicit Finite Difference Method

 

Abstrak. Metode beda hingga eksplisit digunakan untuk mengaproksimasi suatu persamaan diferensial pasial yang aplikasikan untuk menentukan harga opsi. Hasil penelitian ini diketahui bahwa perhitungan harga opsi dengan menggunakan metode beda hingga eksplisit bernilai negatif pada saat partisi N ≥ 25  dengan nilai -2,21. Dengan demikian, hasil perhitungan harga opsi tidak konvergen dan menjauhi hasil solusi analitik perhitungan harga opsi (Black-Scholes). Hal ini disebabkan karena salah satu ketiga probabilitas Bj = 1- σ2j2Δt yaitu  bernilai negatif yaitu (-0.12) saat j ≥ 12 dengan S ≥ 16.25 (dalam satuan). Sehingga metode beda hingga eksplisit ini tidak dapat digunakan untuk menentukan harga opsi.

 Kata Kunci: Harga Opsi, Metode Beda Hingga Eksplisit.

References

[1] Niwiga, D. B., Numerical Methods For The Valuation Of Financial Derivatives, University of Werstern Cape, 2005.
[2] Hull, J. C., Option Future and Other Derivative, Prentice Hall International Inc, 2003.
[3] Wiklund, E., Asian Option Pricing and Volatility, Institute of Technology, 2012.
[4] Causon, D.M. & Mingham, C.G., Introductory Finite Difference Methods for PDEs, Ventus Publishing ApS, 2010.
[5] Nugroho, D.B., Metode Numerik, Universitas Kristen Satya Wacana, 2009.
[6] Hernadi, J., Analisis Real Elementer, Erlangga, 2015.
[7] Wahyudi, Analisis Metode Beda Hingga Implisit, Eksplisit Dan Crank-Nicholson Pada Perhitungan Harga Opsi Asia, UIN Malang, 2014.
UJMC
Published
2019-06-13
How to Cite
Sastro, W. (2019). Analisis Lanjut Metode Beda Hingga Eksplisit Untuk Menentukan Harga Opsi. UJMC (Unisda Journal of Mathematics and Computer Science), 5(01), 41 - 46. https://doi.org/https://doi.org/10.52166/ujmc.v5i01.1302
Issue
Vol 5 No 01 (2019): Unisda Journal of Mathematics and Computer Science (UJMC)
Section
Articles
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