QML- и MCMC-методы оценивания параметров модели стохастической волатильности: применение к российскому рынку ценных бумаг

Экономический журнал Высшей школы экономики. 2026. Т. 30. № 3. С. 457–486.

Borzykh D., Орлов Н. А.

This study compares two estimation approaches for the stochastic volatility (SV) model,
namely quasi-maximum likelihood (QML) and Markov chain Monte Carlo (MCMC). A simula-
tion exercise shows that MCMC delivers markedly more accurate parameter estimates than
QML. However, QML remains substantially faster and far less computationally demanding,
which makes it attractive in large-scale empirical applications. To the best of our knowledge, this
is the first study to estimate an SV model using Russian stock market data. To fill this gap, we
examine securities included in the Moscow Exchange IMOEX index over the period from 1 Janua-
ry 2015 to 1 February 2022. For each stock that was a constituent of the IMOEX as of 1 Feb-
ruary 2022 and had at least three years of trading history, SV model parameters are estimated
using both QML and MCMC methods. The resulting estimates are used to rank stocks by vola-
tility and to classify them into low-, medium-, and high-volatility groups. Economic sectors
are also grouped according to their volatility profiles. The empirical results further indicate that
QML-based estimation systematically understates firm-level risk, which may lead to sizable
losses in portfolio management. The work may be of interest to specialists in financial economet-
rics, as well as macroeconomists and hedge fund employees.
 

Keywords: stochastic volatility model, Russian equity market, MCMC, модель стохастической волатильности, MCMC, SV model, quasi-maximum likelihood method, QML, Markov Chain Monte Carlo method, SV-модель, метод максимального квазиправдоподобия, QML, метод Монте-Карло с цепями Маркова, российский рынок ценных бумаг