Методы и модели в экономике
A.R. Danilishin Risk-neutral dynamics of the asset portfolio by using the principal component method
Динамические системы
Applied aspects in informatics
Системный анализ в медицине
A.R. Danilishin Risk-neutral dynamics of the asset portfolio by using the principal component method

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.


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

DOI: 10.14357/20790279200302

PP. 13-23.

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