DOI: https://doi.org/10.14710/medstat.14.2.183-193

VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION

*Abdul Hoyyi orcid scopus  -  Department of Mathematics, Gadjah Mada University, Indonesia
Abdurakhman Abdurakhman  -  Department of Mathematics, Gadjah Mada University, Indonesia
Dedi Rosadi  -  Department of Mathematics, Gadjah Mada University, Indonesia
Open Access Copyright (c) 2021 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

Citation Format:
Abstract
The Option is widely applied in the financial sector.  The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the  process exponential model. The  process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the  process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK).  The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various  values until convergent result was obtained.
Fulltext View|Download
Keywords: Stochastic process; Black-Scholes-Merton; Le ̀vy process; Variance Gamma; Monte Carlo simulation

Article Metrics:

Article Info
Section: Articles
Language : EN
Recent articles
GSTARI-ARCH MODEL AND APPLICATION ON POSITIVE CONFIRMED DATA FOR COVID-19 IN WEST JAVA MODELING OF LOCAL POLYNOMIAL KERNEL NONPARAMETRIC REGRESSION FOR COVID DAILY CASES IN SEMARANG CITY, INDONESIA A STUDY OF GENERALIZED LINEAR MIXED MODEL FOR COUNT DATA USING HIERARCHICAL BAYES METHOD More recent articles
Most cited articles
IDENTIFIKASI AUTOKORELASI SPASIAL PADA JUMLAHPENGANGGURAN DI JAWA TENGAH MENGGUNAKAN INDEKS MORAN Front-Matter ANALISIS PENGARUH LOKASI DAN KARAKTERISTIK KONSUMEN DALAM MEMILIH MINIMARKET DENGAN METODE REGRESI LOGISTIK DAN CART ANALISIS EFISIENSI BANK PERKREDITAN RAKYAT DI KOTA SEMARANG DENGAN PENDEKATAN DATA ENVOLEPMENT ANALYSIS APLIKASI GENERALIZED SPACE TIME AUTOREGRESSIVE (GSTAR) PADA PEMODELAN VOLUME KENDARAAN MASUK TOL SEMARANG More cited articles
  1. Abdurakhman, A., & Maruddani, D. A. I. (2018). Pengaruh Skewness dan Kurtosis Dalam Model Valuasi Obligasi. Media Statistika, 11(1), 39–51. https://doi.org/10.14710/medstat.11.1.39-51
  2. Avramidis, A. N., & L’Ecuyer, P. (2006). Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing under the Variance Gamma Model. Management Science, 52(12), 1930–1944. https://doi.org/10.1287/mnsc.1060.0575
  3. Avramidis, A. N., L’Ecuyer, P., & Tremblay, P. A. (2003). Efficient Simulation of Gamma and Variance-Gamma Processes. Winter Simulation Conference Proceedings, 1, 319–326. https://doi.org/10.1109/wsc.2003.1261439
  4. Brigo, D., Dalessandro, A., Neugebauer, M., & Triki, F. (2011). A Stochastic Processes Toolkit for Risk Management. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1109160
  5. Clyde, M. A., Ghosh, J., & Littman, M. L. (2011). Bayesian Adaptive Sampling for Variable Selection and Model Averaging. Journal of Computational and Graphical Statistics (Vol. 20, Issue 1). https://doi.org/10.1198/jcgs.2010.09049
  6. Daal, E. A., & Madan, D. B. (2005). An Empirical Examination of the Variance-Gamma Model for Foreign Currency Options. Journal of Business, 78(6), 2121–2152. https://doi.org/10.1086/497039
  7. Dmouj, A. (2004). Stock Price Modelling : Theory and Practice. Masters Degree Thesis, Vrije Universiteit
  8. Finance Yahoo. (2021a). Nokia Corporation (NOK). Finance Yahoo. https://finance.yahoo.com/quote/NOK/options?p=NOK
  9. Finance Yahoo. (2021b). Zoom Video Communications, Inc. (ZM). Finance Yahoo. https://finance.yahoo.com/quote/ZM?p=ZM
  10. Finlay, R., & Seneta, E. (2006). Stationary-increment Student snd Variance-Gamma Processes. Journal of Applied Probability. https://doi.org/10.1239/jap/1152413733
  11. Fragiadakis, K., Karlis, D., & Meintanis, S. G. (2013). Inference Procedures for the Variance Gamma Model and Applications. Journal of Statistical Computation and Simulation, 83(3), 555–567. https://doi.org/10.1080/00949655.2011.624518
  12. Fu, M. C. (2007). Variance-gamma and Monte Carlo. Applied and Numerical Harmonic Analysis. https://doi.org/10.1007/978-0-8176-4545-8_2
  13. Hoyyi, A., Rosadi, D., & Abdurakhman. (2021). Daily Stock Prices Prediction Using Variance Gamma Model. Journal of Mathematical and Computational Science, 11(2), 1888–1903. https://doi.org/10.28919/jmcs/5469
  14. Hull, J. C. (2002). Options, Futures, and Other Derivatives: Solutions Manual. In Asset Pricing (Vol. 59, Issue 2)
  15. Ivanov, R. V. (2018). On Risk Measuring in the Variance-Gamma Model. Statistics and Risk Modeling. https://doi.org/10.1515/strm-2017-0008
  16. Ivanov, R. V., & Ano, K. (2016). On Exact Pricing of FX Options in Multivariate Time-Changed Lévy Models. Review of Derivatives Research. https://doi.org/10.1007/s11147-016-9120-4
  17. Madan, D. B., Carr, P. P., & Chang, E. C. (1998). The Variance Gamma Process and Option Pricing. Review of Finance, 2, 79–105. https://doi.org/10.1023/a:1009703431535
  18. Madan, D. B., & Milne, F. (1991). Option Pricing With V. G. Martingale Components. Mathematical Finance, 1(4), 39–55. https://doi.org/10.1111/j.1467-9965.1991.tb00018.x
  19. Martin, & Maechler. (2019). Package ‘ Bessel ’. Computations and Approximations for Bessel Functions. https://cran.r-project.org/package=Bessel
  20. Permana, F. J., Lesmono, D., & Chendra, E. (2014). Valuation of European and American Options under Variance Gamma Process. Journal of Applied Mathematics and Physics, 02(11), 1000–1008. https://doi.org/10.4236/jamp.2014.211114
  21. Reddy, K., & Clinton, V. (2016). Simulating Stock Prices Using Geometric Brownian Motion: Evidence from Australian companies. Australasian Accounting, Business and Finance Journal, 10(3), 23–47. https://doi.org/10.14453/aabfj.v10i3.3
  22. Scott, A. D., Dong, C. Y., & Scott, M. D. (2018). Package ‘ VarianceGamma ’. The Variance Gamma Distribution. https://cran.r-project.org/package=VarianceGamma
  23. Seneta, E. (2004). Fitting the variance-Gamma Model to Financial Data. Journal of Applied Probability, 41A(5), 177–187. https://doi.org/10.1239/jap/1082552198
  24. Seneta, E., & Madan, D. (1990). The Variance Gamma ( V . G .) Model for Share Market Returns Author ( s ): Dilip B . Madan and Eugene Seneta Source. The Journal of Business , Vol . 63 , No . 4 ( Oct ., 1990 ), pp . 511-524 Published by : The University of Chicago Press Stable URL : htt. 63(4), 511–524
  25. Shreve, S., Chalasani, P., & Jha, S. (1997). Stochastic Calculus and Finance. In FinancialEbooks.NET. https://doi.org/10.1007/bf00052459
  26. Team, R. C. (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. https://www.r-project.org/

Last update:

  1. Special greeks of a variance-gamma driven vasicek model

    Adaobi M. Udoye, Lukman S. Akinola. Scientific African, 19 , 2023. doi: 10.1016/j.sciaf.2022.e01466

Last update: 2024-11-03 02:23:41

No citation recorded.