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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Language : EN
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  1. Ammann, M. & Reich, C. (2001). VaR for Nonlinear Financial Instruments—Linear Approximation or Full Monte Carlo? Financial Markets and Portfolio Management, 15(3), 363–378
  2. Britten-Jones, M. & Schaefer, S. M. (1999). Non-linear Value-at-Risk. Review of Finance, 2(2), 161–187
  3. Castellacci, G. & Siclari, M. J. (2003). The Practice of Delta–Gamma VaR: Implementing the Quadratic Portfolio Model. European Journal of Operational Research, 150(3), 529–545
  4. Chen, H.-Y., Lee, C.-F., & Shih, W. (2010). Derivations and Applications of Greek letters: Review and Integration. Handbook of Quantitative Finance and Risk Management, 491–503
  5. Chen, R. & Yu, L. (2013). A Novel Nonlinear Value-at-Risk Method for Modeling Risk of Option Portfolio with Multivariate Mixture of Normal Distributions. Economic Modelling, 35, 796–804
  6. Cui, X., Zhu, S., Sun, X., & Li, D. (2013). Nonlinear Portfolio Selection using Approximate Parametric Value-at-Risk. Journal of Banking & Finance, 37(6), 2124–2139
  7. Devitasari, P., Maruddani, D. A. I., & Kartikasari, P. (2023). Pengaruh Konveksitas Terhadap Sensitivitas Harga Jual dan Delta-Normal Value at Risk (VaR) Portofolio Obligasi Pemerintah Menggunakan Durasi Eksponensial. Jurnal Gaussian, 11(4), 532–541
  8. Dowd, K. (2007). Measuring Market Risk. England: John Wiley & Sons
  9. Duffie, D. & Pan, J. (2001). Analytical Value-at-Risk with Jumps and Credit Risk. Finance and Stochastics, 5, 155–180
  10. Dziwago, E. (2016). Analiza Wrażliwości Ceny Hybrydowej Korytarzowej Opcji Kupna. Studia Ekonomiczne, 295, 5–18
  11. Gao, P. (2009). Options Strategies with the Risk Adjustment. European Journal of Operational Research, 192(3), 975–980
  12. Hull, J. C. (2003). Options Futures and Other Derivatives. India: Pearson Education India
  13. Jaschke, S. R. (2001). The Cornish-Fisher-Expansion in the Context of Delta-Gamma-Normal Approximations. SFB 373 Discussion Paper
  14. Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk (Third). The United States: The McGraw-Hill Companies, Inc
  15. Lee, S., Li, Y., Choi, Y., Hwang, H., & Kim, J. (2014). Accurate and Efficient Computations for the Greeks of European Multi-asset Options. Journal of the Korean Society for Industrial and Applied Mathematics, 18(1), 61–74
  16. Maruddani, D. A. I. & Abdurakhman, A. (2021). Delta-Normal Value at Risk Using Exponential Duration with Convexity for Measuring Government Bond Risk. DLSU Business and Economics Review, 31, 72–80
  17. Mina, J. & Ulmer, A. (1999). Delta-Gamma Four Ways. RiskMetrics Group
  18. Poncet, P. & Portait, R. (2022). Value at Risk, Expected Shorfall, and Other Risk Measures. In Capital Market Finance: An Introduction to Primitive Assets, Derivatives, Portfolio Management and Risk (pp. 1103–1169). Springer
  19. Rosadi, D. (2009). Diktat Kuliah Manajemen Risiko Kuantitatif. Yogyakarta: UGM
  20. Sulistianingsih, E., Rosadi, D., & Abdurakhman. (2019). Delta Normal and Delta Gamma Normal Approximation in Risk Measurement of Portfolio Consisted of Option and Stock. https://doi.org/10.1063/1.5139181
  21. Wang, X., Xie, D., Jiang, J., Wu, X., & He, J. (2017). Value-at-Risk Estimation with Stochastic Interest Rate Models for Option-Bond Portfolios. Finance Research Letters, 21, 10–20
  22. Yu, X., & Xie, X. (2013). On Derivations of Black-Scholes Greek Letters. Research Journal of Finance and Accounting, 4(6), 80–85

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