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Valuasi Opsi Beli ({\it Call Options}) Eropa bervolatilitas Stokastik dengan menggunakan Modifikasi Metode Karakteristik dan Metode Elemen Hingga

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  • Garnadi, Agah D.

Abstract

Dalam tulisan ini, disajikan pemakaian Metode Elemen Hingga dikombinasikan dengan Modifikasi Metode Karakteristik untuk valuasi opsi beli Eropa bervolatilitas stokastik. Nilai opsi beli Eropa bervolatilitas stokastik ini, dinyatakan sebagai persamaan transport konveksi-diffusi yang berevolusi, dengan koefisien bergantung secara spasial untuk suku konveksi dan diffusinya, sehingga bersifat 'cacat' ({\it degenerate}). Dalam approksimasi waktu, digunakan metode splitting 2-langkah. Pada langkah pertama, digunakan Modifikasi Metode Karakteristik, dan langkah kedua digunakan metode implisit (backward Euler). Sedangkan approksimasi spasial digunakan Metode Elemen Hingga, dengan menggunakan basis elemen bilinear. Penggunaan Modifikasi Metode Karakteristik, memerlukan interpolasi untuk setiap langkahnya, dalam tulisan ini digunakan interpolasi biharmonik. Sebuah kasus dari Opsi beli Eropa untuk pertukaran mata uang asing akan disajikan sebagai contoh untuk hasil numeriknya.

Suggested Citation

  • Garnadi, Agah D., 2017. "Valuasi Opsi Beli ({\it Call Options}) Eropa bervolatilitas Stokastik dengan menggunakan Modifikasi Metode Karakteristik dan Metode Elemen Hingga," INA-Rxiv fhbsx, Center for Open Science.
    • Handle: RePEc:osf:inarxi:fhbsx
    DOI: 10.31219/osf.io/fhbsx
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. P. A. Forsyth & K. R. Vetzal & R. Zvan, 1999. "A finite element approach to the pricing of discrete lookbacks with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 87-106.
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