The Stochastic Properties of Major Canadian Exchange Rates

Abstract

This paper extends the results of Akgiray and Booth [2] on the stochastic properties of five major Canadian exchange rates using the EGARCH‐M model along with the generalized error distribution (GED). In addition to the issue of first‐ and second‐order dependencies, explored by the authors, the paper (1) addresses the issue of asymmetric volatility, (2) examines the extent to which volatility affects future movements in these exchange rates, (3) measures the amount of kurtosis in the data, and (4) investigates the transmission mechanism of innovations and volatility shocks across the five Canadian exchange rate markets. The five Canadian dollar exchange rates are for the U.S. dollar, the Japanese yen, the British pound, the German mark, and the French franc. Changes in Canadian exchange rates are conditionally heteroskedastic, a finding which is in line with that of Akgiray and Booth [2]. There is no evidence supporting the assertion that volatility triggers such changes. The hypothesis of asymmetric volatility is rejected for all Canadian exchange rates; thus unexpected appreciations and depreciations of the Canadian currency have similar impact on future volatility of these exchange rates. Innovations in the Canadian exchange rate markets for the U.S. dollar, the British pound, and French franc influence the Japanese yen market, while innovations in the markets of the British pound and German mark influence the French franc market. Significant but negative volatility spillovers radiate from the German mark market to the U.S. dollar market and from the French franc market to the German mark market, resulting in lower levels of volatility in both the U.S. and German markets. The distributions of all five series of Canadian exchange rates are highly leptokurtic relative to the normal distribution. The GED distribution provides a good characterization of these distributions.

Index futures and options and stock market volatility

“…However, empirical evidence shows that accounting for second moment dependencies is not sufficient to remove the fat tails from the empirical distribution of index stock returns. Consequently, several authors use leptokurtic distributions such as the Student-t distribution [for example, Bollerslev (1987), Baillie and Bollerslev (1989), Akgiray and Booth (1990)], and the generalized error distribution (GED) [e.g., Nelson (1991), Booth, Hatem, Virtanen, and Ylli-Olli (1992), and Theodossiou (1994)]. This article employs the GED because of its ability to accommodate fatter tails and peakedness.…”

Modeling Exchange Rate Volatility: Application of the GARCH and EGARCH Models

“…The GJR model is a simple extension of GARCH with an additional term added to account for possible asymmetries (Brooks [10]) expressed as [19], for the U.S. stock market returns. Likewise, Hsieh [37], Theodossiou [38] and Koutmos & Theodossiou [39] use this model for foreign exchange rates. Indeed, the application of EGARCH suggests that the assumption of normal distribution has been relaxed in modeling the effect of volatility (Ali [40]).…”

Information Flows Between Eurodollar Spot and Futures Markets

“…1 See Theodossiou (1994) and Koutmos and Theodossiou (1994) for the EGARCH model. Our model has a conditional normal distribution assumption.…”