DOI: https://doi.org/10.14710/medstat.16.2.160-169

APPLICATION OF DELTA GAMMA (THETA) NORMAL APPROXIMATION IN RISK MEASUREMENT OF AAPL'S AND GOLD'S OPTION

*Evy Sulistianingsih orcid scopus  -  Department of Mathematics, Universitas Tanjungpura, Jl. Prof. Dr. H. Hadari Nawawi, Pontianak, Indonesia 78124, Indonesia
Shantika Martha orcid  -  Department of Mathematics, Universitas Tanjungpura, Jl. Prof. Dr. H. Hadari Nawawi, Pontianak, Indonesia 78124, Indonesia
Wirda Andani orcid  -  Department of Mathematics, Universitas Tanjungpura, Jl. Prof. Dr. H. Hadari Nawawi, Pontianak, Indonesia 78124, Indonesia
Wiji Umiati  -  Department of Mathematics, Universitas Tanjungpura, Jl. Prof. Dr. H. Hadari Nawawi, Pontianak, Indonesia 78124, Indonesia
Ayu Astuti  -  Department of Mathematics, Universitas Tanjungpura, Jl. Prof. Dr. H. Hadari Nawawi, Pontianak, Indonesia 78124, Indonesia
Open Access Copyright (c) 2023 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
The option value has a nonlinear dependence relationship on risk factors existing in the capital market. Therefore, this paper considered utilizing Delta Gamma (Theta) Normal Approximation (DGTNA) as a nonlinear approach to determine the change of profit/loss of a European call option to assess the option risk. The method uses the second order of Taylor Polynomial around the stock price underlying the option to approximate the option profit/loss, which is crucial to construct the VaR based on DGTNA. VaR based on DGTNA also considered three Greeks, namely Delta, Gamma, and Theta, known as sensitivity measures in option. This research applied VaR based on DGTN approximation to analyze the European call option of Apple Inc (AAPL) and Barrick Gold Corporation (GOLD) for several strike prices. The performance of DGTN VaR analyzed by Kupiec Backtesting summarized that in this case, DGTN VaR provides the best risk assessment over different confidence levels (80, 90, 95, and 99 percent) compared to Delta Normal VaR and Delta Gamma Normal VaR.
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Keywords: Nonlinear-VaR; Derivative; Option-Greek
Funding: Fakultas MIPA Universitas Tanjungpura

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