The use of GARCH models for the calculation of minimum capital risk requirements: International evidence

The paper seeks to explain volatility and risk (VaR) modelling using data from international financial markets, and particularly to evaluate the performance of minimum capital risk requirements (MCRR) estimates in an out‐of‐sample period using the bootstrapping approach.

This paper captures financial time series characteristics by employing the GARCH(p,q) model, and its EGARCH, threshold GARCH (TGARCH), asymmetric component (AGARCH) and component GARCH (CGARCH) extensions. Furthermore, under the bootstrapping approach, the MCRR for long and short positions over five‐day, ten‐day and 15‐day horizon periods is calculated. This paper uses daily data from the USA (Dow Jones, NASDAQ) and European (ASE, Greece; DAX, Germany; FTSE‐100, UK) financial markets.

The results show that higher capital requirements are necessary for a short position since a loss is more likely than for a long position.

Future research should examine the performance of multivariate time series models when using daily and monthly returns of international mature and emerging markets. Consequently, it is of interest to consider multivariate models to describe the volatility and market risk of several time series jointly, to exploit possible linkages that exist.

The findings are strongly recommended to risk managers and modellers dealing with US and European financial markets.

The contribution of this paper is to provide new evidence from international equity markets to the modelling of financial time series by explaining volatility and VaR (MCRR) estimates in the US and European markets. This paper explains the functioning of financial markets and the process by which financing decisions are reached through risk modelling.