Conditional Quantiles of Volatility in Equity Index and Foreign Exchange Data

Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Les idées et les opinions émises sont sous l'unique responsabilité des auteurs, et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents preliminary research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners. This paper uses estimation techniques related to those of Galbraith and Zinde-Walsh (2000) for ARCH and GARCH models, based on realized volatility (Andersen and Bollerslev 1998, and others), to estimate the conditional quantiles of daily volatility in samples of equity index and foreign exchange data. These techniques in principle allow us to characterize the entire conditional distribution of volatility, conditioning on past realized volatility and past squared returns. We take samples of daily and intra-day returns on the Toronto Stock Exchange 35 index, the DM/$ US exchange rate and the Yen/$ US exchange rate. In addition to information about the conditional extremes of volatility, we find some evidence that lower percentiles of the conditional distribution rise proportionately less in high-volatility periods than do the higher percentiles. thank CIRANO (Centre Interuniversitaire de recherche en analyse des organisations), FCAR (Fonds pour la formation de chercheurs et l'aide à la recherche) and the Social Sciences and Humanities Research Council of Canada for financial support. Equity index data were provided by the Toronto Stock Exchange, Market Data Services.