Informatics and Applications
2020, Volume 14, Issue 1, pp 48-55
RISK-NEUTRAL DYNAMICS FOR THE ARIMA-GARCH RANDOM PROCESS WITH ERRORS DISTRIBUTED ACCORDING TO THE JOHNSON'S Su LAW
- A. R. Danilishin
- D. Yu. Golembiovsky
Abstract
Risk-neutral world is one of the fundamental principles of financial mathematics, for definition of a fair value of derivative financial instruments. The article deals with the construction of 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. Methods for finding risk-neutral coefficients require the existence of a generating function of moments (examples of such transformations are the Escher transformation, the extended Girsanov principle). A generating function of moments is not known for Student and Johnson's SU distributions. The authors form a generating function of moments for the Johnson's SU distribution and prove that a modification of the extended Girsanov principle may obtain a risk-neutral measure with respect to the chosen distribution.
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[+] About this article
Title
RISK-NEUTRAL DYNAMICS FOR THE ARIMA-GARCH RANDOM PROCESS WITH ERRORS DISTRIBUTED ACCORDING TO THE JOHNSON'S SU LAW
Journal
Informatics and Applications
2020, Volume 14, Issue 1, pp 48-55
Cover Date
2020-03-30
DOI
10.14357/19922264200107
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 ; 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 Leninskiye Gory, Moscow 119991, GSP-1, Russian Federation
Department of Banking, Sinergy University, 80-G Leningradskiy Prospect, Moscow 125190, Russian Federation
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