Exchange rates and oil prices: A multivariate stochastic volatility analysis

https://doi.org/10.1016/j.qref.2012.01.003Get rights and content

Abstract

This paper uses the multivariate stochastic volatility (MSV) and the multivariate GARCH (MGARCH) models to investigate the volatility interactions between the oil market and the foreign exchange (FX) market, in an attempt to extract information intertwined in the two for better volatility forecast. Our analysis takes into account structural breaks in the data. We find that when the markets are relatively calm (before the 2008 crisis), both oil and FX markets respond to shocks simultaneously and therefore no interaction is detected in daily data. However, during turbulent time, there is bi-directional volatility interaction between the two. In other words, innovations that hit one market also have some impact on the other at a later date and thus using such a dependence significantly improves the forecasting power of volatility models. The MSV models outperform others in fitting the data and forecasting exchange rate volatility. However, the MGARCH models do better job in forecasting oil volatility.

Highlights

► This paper models the volatilities of exchange rates and oil using MSV and MGARCH models. ► Both oil and FX markets respond to shocks simultaneously in normal time. ► There is bi-directional volatility interaction between markets inturbulent time. ► MSV models outperform others in fitting the data and forecasting exchange rate volatility. ► MGARCH models do better job in forecasting oil volatility.

Introduction

It is well-known that oil prices and the U.S. dollar exchange rates are highly correlated. Given the fact that oil is quoted in U.S. dollars, it is natural to hypothesize that exchange rates drive oil prices. More specifically, other things equal, when the U.S. dollar depreciates, oil-exporting countries would raise oil prices in order to stabilize the purchasing power of their (U.S. dollar) export revenues in terms of their (predominately) euro-denominated imports. This is equivalent to a reduction in supply or a leftward shift in the supply curve. On the demand side, the U.S. dollar depreciation makes oil less expensive for consumers in other countries (in local currency), thereby increasing their crude oil demand. Both effects, the reduction in supply and the increase in demand, cause an increase in oil prices denominated in U.S. dollars. The exchange-rate-to-oil-price causality relationship is supported by the empirical evidence found in Zhang, Fan, Tsai, and Wei (2008), Krichene (2005), and Yousefi and Wirjanto (2004).

From the other perspective, exchange rates are believed to be determined by expected future fundamental conditions, among which oil is surely an important factor. Increasing oil prices lead to stronger economies for oil-exporters and higher production costs for oil-importers, hence it would cause the appreciation of oil-exporter currencies relative to those of oil-importers. So, it is likely that the causality runs from oil prices to the exchange rate. Benassy-Querea, Mignonb, and Penot (2007), Coudert, Mignon, and Penot (2007), Chen and Chen (2007), Ayadi (2005), Chaudhuri and Daniel (1998) and Krugman (1984) all provide evidence supporting this view.

These studies, despite their mixed implications, tend to suggest that oil prices and exchange rates probably both contain information that can affect each other. Accordingly, Chen, Rogoff, and Rossi (2008) and Groen and Pesenti (2010) use exchange rates to obtain a better forecast of oil (and other commodities) prices, while Amano and Norden (1998) improve the exchange rate forecast by including oil price in the model.

The current literature that examines the relationship between oil price and exchange rate, as cited above, mainly focuses on their returns. As noted by Clark (1973), Tauchen and Pitts (1983), and Ross (1989), the volatility of an asset is also related to the rate of information flow across interacted markets. So the link between the oil and the FX markets should appear not only in return but also in volatility. Examining the volatility interaction between exchange rates and oil prices can shed light on the direction of the causality relationship from a new perspective. Furthermore, if a significant connection does exist, extracting and using the information intertwined in both markets would improve forecasts of exchange rate and oil volatilities, which are critical in many areas of modern finance.

Instead of focusing on the relationship between exchange rate and oil returns, which many papers cited above have investigated, this paper first examines how volatilities of oil and FX markets interact. Second, the paper attempts to extract information intertwined in the two markets, if detected, for a better forecast of the exchange rate and oil volatilities.

Using the optimal lag-length algorithm with the Bayesian information criterion (BIC), we posit a bivariate model of vector of autoregression VAR(1) with stochastic volatility for the joint processes governing the returns of various exchange rates and the oil prices. We model the stochastic volatility using both the multivariate stochastic volatility (MSV) and the conditional correlation multivariate GARCH (CC-MGARCH) models. We fit two variants of the models: the constant conditional correlation and the dynamic conditional correlation to identify the better one for the data. For comprehensive discussion of the MSV and the CC-MGARCH, the reader is referred to Asai, McAleer, and Yu (2006) and Bauwens, Laurent, and Rombouts (2006). To estimate the MSV models, we use the Bayesian Markov chain Monte Carlo (MCMC) method by Jacquier, Polson, and Rossi (1994) and Kim, Shephard, and Chib (1998). For the CC-MGARCH models, we use the maximum likelihood methods proposed by Bollerslev (1990) and Engle (2002). To investigate whether structural breaks have occurred in the time series, we use the generalized M-fluctuation framework suggested by Kuan and Hornik (1995). Our tests indicate that there is a break in all variance series. Using the dynamic programming algorithm suggested by Bai and Perron (2003), we identify the break date around September 11, 2008 when Lehman Brothers was about to collapse. Thus, to account for structural break, we divide the data into two sub-samples with the break point and use each to fit the models under investigation.

Our empirical results show that during normal time (before the 2008 financial crisis,) markets are quite efficient. Shocks to one market are quickly transmitted and incorporated into the price in the other market. Therefore, we cannot detect the volatility interaction between the two markets in daily data. However, during the peak time of the financial crisis in 2008, it seems that information from one market is incorporated into the price in the other market more slowly. Therefore, we can detect the bidirectional interaction in volatility between the two markets in daily data during this period. Our result is consistent with the findings of Razgallah and Smimou (2011) that the interaction between the two markets is more significant during volatile periods. This nonlinearity of the relationship can be attributed to inefficient information incorporation during market chaos. During the periods when there is significant interaction between the markets, information in one market is useful in forecasting volatility in the other. As a result, we find that the multivariate models outperform the univariate counterparts in terms of forecasting. In addition, we show that the MSV models do a better job in forecasting FX volatility but the MGARCH models forecast better oil volatility.

The remainder of the paper is organized as follows. Section 2 describes the data set and conducts a preliminary analysis of the data. Section 3 discusses the models. Section 4 explains estimation methodology. Section 5 presents estimation results. Section 6 checks the models in terms of goodness-of-fit and evaluates their forecast power, and Section 7 concludes the paper.

Section snippets

Data and preliminary analysis

The data set used in this study consists of a daily oil spot price time series and nine daily time series of exchange rates against the U.S. dollar, including the Canadian dollar (CAD), the Norwegian krone (NOK), the euro (EUR), the Indian rupee (INR), the Japanese yen (JPY), the Singaporean dollar (SGD), the Brazilian real (BZR), the Mexican peso (MXP), and the U.S. dollar trade weighted index (USX). The Canadian dollar, Norwegian krone and Mexican peso are chosen to represent the exchange

The model

Based on the preliminary analysis in the previous section and using the optimal lag-length algorithm with the Bayesian information criterion (BIC), we posit the bivariate VAR(1) with stochastic volatility models for the joint processes governing the exchange rates and the oil returns. For comparison, we use both the bivariate SV and the bivariate GARCH(1,1) to model the joint volatility process. Two variants of the multivariate volatility models, the constant conditional correlation and the

Estimation methodology

We use a two-step estimation method. First, we estimate the mean (Eq. (1)) and extract the residuals. In the second step, we use the residuals to estimate the volatility. To test for structural break in volatility, which is the squared residual, we use the generalized M-fluctuation framework suggested by Kuan and Hornik (1995). The test involves constructing an empirical fluctuation process, governed by a functional central limit theorem, which captures fluctuation over time. The process is

CCC-MSV model

Table 3 reports the estimates of the following CCC-MSV model for the first sub-sample.ete=exphte2ϵte,eto=exphto2ϵto,ρ=cov(ϵte,ϵto)ht+1e=μe+ϕee(hteμe)+ϕeo(htoμo)+ηte,ηteiidN(0,σe2),ht+1o=μo+ϕoe(hteμs)+ϕoo(htoμo)+ηto,ηtoiidN(0,σo2).

We observe that both exchange rate and oil volatilities are very persistent. The persistent coefficient for exchange rates ϕee ranges from.7457 for USD/NOK to.9780 for USD/CAD. For oil, ϕoo varies from.8376 to.9412. These results are consistent with the fact that

Model checking

In this section, we check the goodness-of-fit of each model and compare them. To check the goodness-of-fit, we test whether the volatility in each market, indicated by each model, is sufficient in explaining the stylized facts, such as heavy tail, volatility clustering. In particular, we test if the residuals, having been standardized by the corresponding volatility in the variance equations, are standard normal. Table 11, Table 12 present the test results.

Table 11 reports various statistics of

Conclusion

This paper studies the volatility interaction between the oil market and the FX market in an attempt to extract information intertwined in the two for better volatility forecasting. We employ the multivariate stochastic volatility as well as the multivariate GARCH framework, allowing the volatility in one market to Granger-cause that in the other. To account for structural breaks in the series, we first identify the break point and then use it to divide the time series into sub-samples and

Acknowledgment

We thank Jens Christensen, Allen Bellas, two anonymous referees, seminar participants at the Metropolitan State University Faculty Seminar, and session participants at the 2011 WEAI meeting for valuable comments and suggestions which have helped us significantly improve the paper. All remaining errors rest with us.

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