Methods and models in economy
A.R. Danilishin Risk-neutral dynamics of the asset portfolio by using the principal component method
Dynamical Systems
Applied aspects in informatics
Системный анализ в медицине
A.R. Danilishin Risk-neutral dynamics of the asset portfolio by using the principal component method
Abstract. 

Assessing the risks of a portfolio of options on various underlying assets requires a modeling of the joint price dynamics of these assets. In the case of a large number of assets, the principal component method is often used to reduce the dimension, which allows to model prices of underlying assets by modeling relatively small number of uncorrelated components. The ARIMA-GARCH model is considered for modeling dynamics of main components of underlying asset’s prices, because of it allows to take into account changes in the trend and volatility of random processes. Monte Carlo option risk assessment is carried out on the basis of both physical and risk-neutral measures. This is due to the fact that risk metrics based on a physical measure are retrospective, which makes it difficult to predict future price risks of financial instruments. Method of transforming ARIMA-GARCH coefficients that provide risk-neutral dynamics of underlying asset’s prices is produced in this article.

Keywords: 

ARIMA, GARCH, risk-neutral measure, extended Girsanov principle, Johnson’s SU distribution, option pricing, principal component analysis.

DOI: 10.14357/20790279200302

PP. 13-23.
 
References

1. Hull J. Options, Futures, and Other Derivatives. 10th Edition. Canada: Pearson, 2018.
2. Rockafeller T., Uryasev S. Optimization of conditional value - at – risk // The J. Risk, 2000. Vol. 3. P. 21-41.
3. Bollerslev T. Generalized autoregressive conditional heteroskedasticity // Journal of Economet-rics, 1986. Vol. 52. P. 5-59.
4. Elie L., Jeantheau T. Consistency in Heteroskedastic Models // Comptes rendus de l’Académie des Sciences, 1995. Vol. 320. P. 1255-1258.
5. Duan J. The GARCH Option Pricing Model // Mathematical Finance, 1995.
6. Elliott Robert J., Madan Dilip B. A Discrete Time Equivalent Martingale Measure // Mathematical Finance, 1998. Vol. 8, N 2. P. 127-152. doi: 10.1111/1467-9965.00048.
7. Pearson K. On lines and planes of closest fit to systems of points in space // Phil, 1901. P. 559-572. doi: 10.1080/14786440109462720.
8. Tilman L., Golub B. Measuring yield curve risk using principal components analysis, value at risk, and key rate durations // The Journal of Portfolio Management, 1997. Vol. 23, N 4. P. 72-84.
9. Specht K., Gohout W. Portfolio selection using the principal components GARCH model // Financial Markets and Portfolio Management, 2003. Vol. 17, N 4. P. 450-458. doi: 10.1007/s11408-003-0404-y.
10. Geng J. Principal Component GARCH Model // SSRN Electronic Journal, 2007. doi: 10.2139/ssrn.1068945.
11. Dubrov A, Mhitaryan V, Troshin L.I. Mnogomernye statisticheskie metody i osnovy ekonometriki [Multidimensional statistical methods and fundamentals of econometrics]. Moscow: MESI; 2002.
12. Williams D. Probability with Martingales. Cambridge: Cambridge University Press, 1991.
13. Bell D. Transformations of measures on an infinite-dimensional vector space. In: Сinlar. E., Fitzsimmons P.J., Williams R.J. Seminar on Stochastic Processes // Progress in Probability, 1990. Vol. 24. P. 15-25. doi:10.1007/978-1-4684-0562-0_3.
14. Yi Xi. Comparison of option pricing between ARMA-GARCH and GARCH-M models. USA: University of Western Ontario, 2013. MoS Thesis.
15. Terasvirta, T. An Introduction to Univariate GARCH Models // Handbook of Financial Time Series, 2009. Vol. 10. P. 17-42. doi:10.1007/978-3-540-71297-8_1.
16. Akgiray V. Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts // The Journal of Business, 1989. Vol. 62, N 1. P. 55-80. doi:10.1086/296451.
17. Danilishin A, Golembiovsky D.Y. Riskneytral’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]. Informatica I ee Primeneniya, 2020; V. 14, 1. P. 48-55. doi: 10.14357/19922264200107.
18. Bollerslev T. Conditionally heteroskedastic time series model for speculative prices and rates of return // The Review of Economics and Statistics, 1987. Vol. 69, N 3. P. 542-547. doi:10.2307/1925546.
19. Simonato J. GARCH processes with skewed and leptokurtic innovations: Revisiting the JohnsonSU case, 2012. Available at: https://ssrn.com/abstract=2060994.
20. Phelim P. Options: A Monte Carlo approach // Journal of Financial Economics, 1977. Vol. 4, N 3. P. 323–338. doi: 10.1016/0304-405X(77)90005-8.
21. Lopez J. Regulatory evaluation of value-at-risk models // Journal of Risk, 1998. Vol. 1, N 2. P. 37- 63. doi: 10.21314/JOR.1999.005.
22. Kupiec P. Techniques for Verifying the Accuracy of Risk Management Models // The Journal of Derivatives, 1995. Vol. 3, N 2. P. 73-84. doi: 10.3905/jod.1995.407942.
 
2024-74-3
2024-74-2
2024-74-1
2023-73-4

© ФИЦ ИУ РАН 2008-2018. Создание сайта "РосИнтернет технологии".