Valuasi harga opsi valuta asing berdasarkan asumsi distribusi hyperbolic = Valuation of currency option using the hyperbolic distribution assumption

Utama, Cantika Puteri (2013) Valuasi harga opsi valuta asing berdasarkan asumsi distribusi hyperbolic = Valuation of currency option using the hyperbolic distribution assumption. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Asumsi distribusi dari return aset yang mendasari suatu opsi perlu dibuat untuk menentukan nilai dari opsi tersebut. Berdasarkan penelitian sebelumnya, asumsi return saham berdistribusi hyperbolic dinyatakan lebih tepat dibandingkan dengan asumsi normal pada formula Black-Scholes. Harga opsi saham dengan asumsi tersebut juga dinyatakan lebih menyerupai harga opsi pasar jika dibandingkan dengan harga opsi yang ditentukan dengan formula Black-Scholes. Berdasarkan penelitian tersebut, pada tugas akhir ini akan dilakukan analisis terhadap opsi valuta asing. Signifikansi return valuta asing berdistribusi hyperbolic akan dilakukan terlebih dahulu dengan menggunakan beberapa metode pengujian, seperti density probabililty plot dan uji khi-kuadrat. Selanjutnya pembangunan model untuk menentukan nilai opsi valuta asing dengan asumsi distribusi hyperbolic dilakukan. Model tersebut mengasumsikan bahwa pergerakan valuta asing mengikuti standardize hyperbolic Levy motion. Setelah pembangunan model, penentuan nilai opsi valuta asing dengan menggunakan model tersebut dan formula Black-Scholes pun dilakukan. Harga opsi dengan menggunakan kedua model tersebut kemudian dibandingkan dengan harga opsi pasar dan diuji signifikansinya dengan menggunakan metode pengujian Wilcoxon signed-rank test. Hasil penulisan tugas akhir ini menunjukkan bahwa return valuta asing secara signifikan dapat dikatakan mengikuti distribusi hyperbolic, namun harga call opsi dengan asumsi tersebut tidak lebih menyerupai harga opsi pasar apabila dibandingkan dengan harga call opsi yang ditentukan dengan formula Black-Scholes. / Distributional assumption for the return on underlying asset of an option plays a key role in the valuation of the option. According to the previous research, it shows that stock returns follows hyperbolic distribution rather than the normal distribution. It also shows that the option prices under the hyperbolic distribution assumption are more similar to the market option price if they are compared to the option prices using the normal distribution assumption in the Black-Scholes formula. From that research, this research will analyze the option with currency as its underlying asset. First, the distribution of currency return will be determined using the density probability plot and chi-square test. Next, the Mathematics model using the hyperbolic distribution assumption to determine the value of an option will be done. The model assumes that the movement of the currency follows the standardize hyperbolic Levy motion. After that, the call option price determined by hyperbolic model and Black-Scholes formula will be calculated. Finally, the call option price from both of the model will be tested against the market option price to see the difference. This significance test are conducted using the Wilcoxon signed-rank test. The result of this research shows that the currency return can significantly be said to follow the hyperbolic distribution. However, the model using the hyperbolic distribution assumption does not give the call option price that is more similar to the market price if it is compared with the call option price using the Black-Scholes formula.

Item Type: Thesis (Bachelor)
Creators:
CreatorsNIMEmail
Utama, Cantika PuteriNIM11220090007UNSPECIFIED
Contributors:
ContributionContributorsNIDN/NIDKEmail
Thesis advisorSaputra, Kie Van IvankyNIDN0401038203kie.saputra@uph.edu
Thesis advisorKim, Sung SukNIDN8963400020sungsuk.kim@uph.edu
Additional Information: SK 112-09 UTA v
Uncontrolled Keywords: valuasi opsi valuta asing; distribusi hyperbolic; hyperbolic Levy motion; formula black-scholes
Subjects: Q Science > QA Mathematics
Divisions: University Subject > Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics
Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics
Depositing User: Mrs Veronica Fitri Astuti
Date Deposited: 12 May 2021 14:17
Last Modified: 02 Nov 2023 09:06
URI: http://repository.uph.edu/id/eprint/18294

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