This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyze spillovers in the values at risk (VaR) between a market index and financial institutions. We construct impulse-response functions for the quantiles of a sample of 230 financial institutions around the world and study how financial institution-specific and system-wide shocks are absorbed by the system. We show how the long-run risk of the largest and most leveraged financial institutions is very sensitive to market wide shocks in situations of financial distress, suggesting that our methodology can prove a valuable addition to the traditional toolkit of policy makers and supervisors.
Bibliographical noteFunding Information:
We would like to thank Peter Christoffersen, Rob Engle, Demian Pouzo, Rossen Valkanov, as well seminar participants at the ECB, the Fourth Annual SoFiE Conference in Chicago, the Cass Business School, the London Business School, the Fourth Tremblant Risk Management Conference, the Vienna Graduate School of Finance and the Fourteenth International Korean Economic Association Conference. We are also grateful to two anonymous referees and Co-Editor Yacine Ait-Sahalia for their invaluable comments which substantially improved the paper. Francesca Fabbri and Thomas Kostka provided data support. The phrase “VAR for VaR” was first used by Andersen et al. (2003) , in the title of their section 6.4. The views expressed in this paper are those of the authors and do not necessarily reflect those of the European Central Bank or the Eurosystem. Tae-Hwan Kim is grateful for financial support from the National Research Foundation of Korea — a grant funded by the Korean Government ( NRF-2009-327-B00088 ).
© 2015 Elsevier B.V.
All Science Journal Classification (ASJC) codes
- Economics and Econometrics