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Valuation of European and American Options under Variance Gamma Process

Geometric Brownian Motion (GBM) is widely used to model the asset price dynamics. Option price
models such as the Black-Sholes and the binomial tree models rely on the assumption that the
underlying asset price dynamics follow the GBM. Modeling the asset price dynamics by using the
GBM implies that the log return of assets at particular time is normally distributed. Many studies
on real data in the markets showed that the GBM fails to capture the characteristic features of asset
price dynamics that exhibit heavy tails and excess kurtosis. In our study, a class of Levy process,
which is called a variance gamma (VG) process, performs much better than GBM model for modeling
the dynamics of those stock indices. However, valuation of financial instruments, e.g. options,
under the VG process has not been well developed. Here, we propose a new approach to the valuation
of European option. It is based on the conditional distribution of the VG process. We also apply
the path simulation model to value American options by assuming the underlying asset log return
follow the VG process. Such a model is similar with that proposed by Tiley [1]. Simulation
study shows that the proposed method performs well in term of the option price.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF APPLIED MATHEMATICS AND PHYSICS; Applied Mathematics and Physics; Vol.2, 2014

No. Panggil

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Penerbit

China : Scientific Research Publishing., 2014

Deskripsi Fisik

p. 1000 - 1008

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

AMERICAN OPTIONS
EUROPEAN OPTIONS
GEOMETRIC BROWNIAN MOTION
VARIANCE GAMMA PROCESS

Info Detail Spesifik

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Pernyataan Tanggungjawab

Ferry Jaya Permana, Dharma Lesmono, Erwinna Chendra

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