Informatics and Applications
2020, Volume 14, Issue 4, pp 83-90
ESTIMATING THE FAIR VALUE OF OPTIONS BASED ON ARIMA-GARCH MODELS WITH ERRORS DISTRIBUTED ACCORDING TO THE JOHNSON'S SU LAW
- A. R. Danilishin
- D. Yu. Golembiovsky
Abstract
In continuation of the article " Risk-neutral dynamics for the ARIMA-GARCH (autoregressive integrated moving average - generalized autoregressive conditional heteroskedasticity) random process with errors distributed according to the Johnson's SU law," this paper presents the experimental results for the ARIMA-GARCH (autoregressive integrated moving average - generalized autoregressive conditional heteroskedasticity) models with normal (N), exponential beta ofthe second type (EGB2), and SU Johnson (JSU) error distributions. The fair value of European options is estimated by the Monte-Carlo method based on the results obtained in the specified article by using the extended Girsanov principle. The parameters of the ARIMA-GARCH-N, ARIMA-GARCH-EGB2, and ARIMA-GARCH-JSU models were found by the quasi-maximum likelihood method. The efficiency of the resulting risk-neutral models was studied using the example of European exchange-traded options PUT and CALL on basic assets DAX and Light Sweet Crude Oil.
[+] References (12)
- Danilishin, A.R., and D.Y. Golembiovsky. 2020. Risk-neytral’naya
dinamika dlya ARIMA–GARCH modeli
s oshibkami, raspredelennymi po zakonu SU Dzhonsona.
[Risk-neutral dynamics for ARIMA–GARCH random process with errors distributed according to the Johnson’s
SU law]. Informatika i ee Primeneniya — Inform. Appl.
14(1):56–62
- Bollerslev, T. 1987. A conditionally heteroskedastic time
series model for speculative prices and rates of return. Rev. Econ. Stat. 69(3):542-547. doi: 10.2307/ 1925546.
- Akgiray, V. 1989. Conditional heteroscedasticity in time series of stock returns: Evidence and forecasts. J. Bus. 62(1):55-80. doi: 10.1086/296451.
- Follmer, H., and A. Schied. 2002. Stochastic finance: An introduction in discrete time. Berlin: Walter de Gruyter. 422 p.
- Terasvirta, T. 2009. An introduction to univariate GARCH models. Handbook of financial time series. Eds. T. G. Andersen, R.A. Davis, J.-P. Kreiss, and Th. V. Mikosch. Berlin-Heidelberg: Springer. 10:17-42. doi: 10.1007/978-3-540-71297-8.1.
- Elliott, R. J., and D.B. Madan. 1998. A discrete time equivalent martingale measure. Math. Financ. 8(2):127- 152. doi: 10.1111/1467-9965.00048.
- Yi, Xi. 2013. Comparison of option pricing between ARMA-GARCH and GARCH-M models. London, Ontario, Canada: University of Western Ontario. MoS Thesis. 73 p.
- Christian, F, andM. Francq. 2019. GARCH models: Structure, statistical inference and financial applications. New York, NY: Wiley. 504 p.
- Boyle, P. 2012. Options: A Monte Carlo approach. J. Financ. Econ. 4(3):323-338. doi: 10.1016/0304- 405x(77)90005-8.
- Hull, J. 2018. Options, futures, and other derivatives. 10th ed. Pearson. 896 p.
- Williams, D. 1991. Probability with martingales. Cambridge: Cambridge University Press. 251 p.
- Bell, D. 1991. Transformations of measure on an infinite dimensional vector space. Seminar on stochastic processes, 1990. Eds. E. Qinlar, P. J. Fitzsimmons, and R. J. Williams. Progress in probability book ser. Boston, MA: Birkhauser. 24:15-25. doi: 10.1007/978-1-4684- 0562-0_3.
[+] About this article
Title
ESTIMATING THE FAIR VALUE OF OPTIONS BASED ON ARIMA-GARCH MODELS WITH ERRORS DISTRIBUTED ACCORDING TO THE JOHNSON'S SU LAW
Journal
Informatics and Applications
2020, Volume 14, Issue 4, pp 83-90
Cover Date
2020-12-30
DOI
10.14357/19922264200412
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
ARIMA; GARCH; risk-neutral measure; Girsanov extended principle; Johnson's SU distribution; option pricing
Authors
A. R. Danilishin  and D. Yu. Golembiovsky , 
Author Affiliations
Department of Operations Research, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskie Gory, Moscow 119991, GSP-1, Russian Federation
Department of Banking, Sinergy University, 80-G Leningradskiy Prosp., Moscow 125190, Russian Federation
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