This study primarily aimed to apply a novel, advanced stochastic volatility model incorporating leverage and an asymmetrically heavy-tailed distribution (ASV-GHskw) to 18 financial asset returns, including 10 Asia-Pacific and six European stock market returns and two crude oil market returns. The study employed a generalized hyperbolic skew student's t-distribution using the Bayesian approach. The study's secondary aim was to concentrate on one-day-ahead downside market risk measurement of the related financial asset returns under Basel Ⅳ regulations based on the ASV-GHskw model. For comparison, an asymmetric stochastic volatility model with a symmetric student's t-distribution (ASV-st) was also considered. The findings indicated that the proposed Bayesian Markov chain Monte Carlo (MCMC) approach was sufficiently efficient, especially when estimating the ASV-GHskw model parameters. Further, the ASV-GHskw model provided a better fit for all financial asset returns examined than its competing ASV-st model. Moreover, the results revealed that the financial institutions taking positions in the examined financial markets will be required to hold additional regulatory capital for market risk exposures under the latest Basel capital regulations. Lastly, the findings give valuable information for risk-averse investors interested in the examined financial markets, as they expect to receive higher-than-average returns by holding less-risky assets.
Citation: Onder Buberkoku. Bayesian analysis of a novel sophisticated stochastic volatility model: A comprehensive empirical application to stock and crude oil markets price returns[J]. AIMS Mathematics, 2026, 11(3): 7400-7435. doi: 10.3934/math.2026304
This study primarily aimed to apply a novel, advanced stochastic volatility model incorporating leverage and an asymmetrically heavy-tailed distribution (ASV-GHskw) to 18 financial asset returns, including 10 Asia-Pacific and six European stock market returns and two crude oil market returns. The study employed a generalized hyperbolic skew student's t-distribution using the Bayesian approach. The study's secondary aim was to concentrate on one-day-ahead downside market risk measurement of the related financial asset returns under Basel Ⅳ regulations based on the ASV-GHskw model. For comparison, an asymmetric stochastic volatility model with a symmetric student's t-distribution (ASV-st) was also considered. The findings indicated that the proposed Bayesian Markov chain Monte Carlo (MCMC) approach was sufficiently efficient, especially when estimating the ASV-GHskw model parameters. Further, the ASV-GHskw model provided a better fit for all financial asset returns examined than its competing ASV-st model. Moreover, the results revealed that the financial institutions taking positions in the examined financial markets will be required to hold additional regulatory capital for market risk exposures under the latest Basel capital regulations. Lastly, the findings give valuable information for risk-averse investors interested in the examined financial markets, as they expect to receive higher-than-average returns by holding less-risky assets.
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Figures(10) / Tables(13)
Onder Buberkoku. Bayesian analysis of a novel sophisticated stochastic volatility model: A comprehensive empirical application to stock and crude oil markets price returns[J]. AIMS Mathematics, 2026, 11(3): 7400-7435. doi: 10.3934/math.2026304
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