Modelling dependence and systemic risk between oil prices and BSE sectoral indices using stochastic copula and CoVar, ΔCoVar and MES approaches

ABSTRACT

We investigate the dependency, risk spillovers, and systemic risk between the sectoral indices returns of the Bombay stock exchange (BSE) and oil prices using recently developed empirical techniques. The dependence is modelled using the time varying Stochastic Autoregressive Copulas (SCAR). Conditional value-at-risk (CoVaR), ΔCoVaR and marginal expected shortfall (MES) measures are used to examine the systemic risk. We find rotated Gumbel and normal copulas to be the best fitting in our analysis. Sectors such as energy, power, and industrial exhibit higher persistence in dependence structure compared to other sectors. Our results reveal that the underlying forces of the dependence between oil prices with other industries vary across time, albeit not so much during stable periods, but increase remarkably during turbulent times. All sectors are affected significantly by extreme oil price movements. The average short-run MES is highest for the metals, materials, and industrials sectors. The lowest average short-run MES values are observed for the fast-moving consumer goods, auto, and carbon sectors. Our risk analysis results reveal that Indian stock sectors are not resistant to oil shocks and there exists significant systemic risk between these markets and the crude oil market.

KEYWORDS:

• Oil prices
• stock prices
• CoVar
• SCAR copula
• systemic risk

JEL CLASSIFICATION:

• C58
• G15
• Q43

Acknowledgments

We thank the anonymous reviewers for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ https://www.cia.gov/library/publications/the-world-factbook/fields/335rank.html

² https://data.worldbank.org/indicator/NY.GDP.MKTP.CD?year_high_desc = true

³ https://www.eia.gov/tools/faqs/faq.php?id=709&t=6

⁴ https://www.cia.gov/library/publications/the-world-factbook/rankorder/2243rank.html

⁵ The new policies scenario assumes government policies recently announced regarding energy policy and targets will be implemented.

⁶ The early version of this paper was released in 2011

⁷ https://www.geographyandyou.com/science/energy/petroleum-pricing-india/

⁸ See Kupiec (2002) and Jorion (2007) for overviews.

⁹ Since we focus on the left-tail risk, we set q to be 1%.

¹⁰ Standard (ordinary least squares [OLS]) regressions estimate the mean of the distribution of the dependent variable Xⁱ, given the explanatory variables X^oil.:

¹¹ Please note that the estimation of CoVaR and ∆CoVaR based on DCC model via equation (17)(17) $CoVa{R}_{q,t}^{i/oil}={\mathrm{\Phi }}^{-1}\left(q\right){\sigma }_t^i\sqrt{1-{\rho }_{ioil,t}^2}+{\mathrm{\Phi }}^{-1}\left(q\right){\rho }_{ioil,t}{\sigma }_t^{oil},$(17) is appropriate for bivariate normal distribution, and it is contrary to copula models. The situation of MES is similar. Furthermore, one has to remember that CoVaR or ∆CoVaR are not estimated via OLS method but they are estimated based on DCC GARCH models based on the framework of Brownlees and Engle (2017) while ∆CoVaR has also been estimated using quantile regression following Adrian and Brunnermeier (2016).