Co-jump between crude oil market and Euro/Dollar exchange rate

Fredj Jawadi1 University of Evry & EconomiX, France [email protected] Waël Louhichi ESSCA School of Management, France, France [email protected] Hachmi Ben Ameur INSEEC Business School, France [email protected] Abdoulkarim IDI CHEFFOU (EDC Paris Business School, France) [email protected]

First Draft, Please do not quote

Abstract

The aim of this paper is to examine volatility co-movement between oil market and Euro/Dollar foreign exchange market. We use recent intraday data to investigate the instantaneous intraday linkage between the two markets. Specifically, we investigate the spillover of extreme price changes (jumps) from the foreign market to the oil market. Our intraday analysis reveals several results. First, we show that there is a volatility spillover from the foreign exchange market to the oil market. Second, intraday jumps occurred in the foreign 1

Corresponding author: Fredj Jawadi, University of Evry, France. Email: [email protected].

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market have a significant impact on oil market conditional volatility. Finally, we show that intraday jumps occur simultaneously in the Euro/Dollar foreign market and in the oil market, which validates the hypothesis of co-jump.

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1. Introduction It’s a well-known fact that oil price shocks are a contributing factor of economic crises as shown in 1973. Since the seminal work of Hamilton (1983), several studies have focused on the impact of oil price changes on the economic activity. The author highlights a significant link between increase in the price of crude oil and U.S. recessions over the period 1948-1972. Burbridge and Harrison (1984) have considered the economies of the USA, Japan, Germany, UK and Canada. Using a VAR models, the authors detect a strong impact of oil price shocks on domestic economic variables. Gisser and Goodwin (1986) use Hamilton’s data and find a positive relation between oil prices and unemployment. Uri (1996) shows that the preceding findings are available for the agricultural sector. While the above studies have considered the impact of oil price changes on economic indicators, in this work we focus on the determinants of oil market volatility. Specifically, we examine the intraday volatility dependence between oil market and Euro/Dollar foreign Exchange market. The relationship between oil prices and US dollars exchange rates is explicated by the following intuition. In fact, international crude oil trading are quoted in US dollars. Therefore, we expect that there is causality link between US dollar exchange rate and crude oil prices. Accordingly, an appreciation of US dollar exchange rate increases the oil price for foreigner in their local currency, which leads to a decrease of oil demand and decreases oil price. Inversely, a weaker US dollar currency triggers an increase of oil demand, which causes a rise in oil price. Therefore, we expect a negative relationship between oil price and US dollars exchange rate. Empirically, several papers have examined the link between these two markets. Using a structural VAR model, Akram (2009) find that weaker dollar exchange rate leads to an increase in oil prices. Reboredo and Rivera-Castro (2013) investigate the relationship between oil prices and US dollar exchange rates using Wavelet multi-resolution analysis. They 3

highlight a negative dependence between the two markets during crisis period. Beckmann and Czudaj (2013) focus on the causality pattern between oil prices and currencies. They find that the most important causality runs from exchange rates to oil prices. Bénassy-Quéré Mignon and Penot (2007) find that 4.3% appreciation of the dollar coincides with 10% rise in oil price. Tantatape et al. (2014) investigate the relationship between the U.S. imported crude oil prices and exchange rates. They show that, in the short-run, exchange rates Granger-causes the price of crude. Moreover, this study reveals that the impulse response of the crude oil price to exchange rate shock is negative and significant. However, oil price shocks have no impact on the exchange rate. Jammazi et al. (2015) examine the link between US dollar exchange rates against 18 currencies and crude oil prices. The authors highlight an asymmetric pass-through from exchange rates to oil prices in the short-run as well as in the long-run. It seems that that negative exchange rate shocks have more impact on oil prices than positive shocks. The above works focus on the first moment (prices and returns). Another corpus of studies has investigated the volatility dependence between the oil market and the foreign market. Zhang et al. (2008) assume that there is no volatility spillover between US dollars exchange rate on oil market. Salisu and Mobolaji (2013) find a bidirectional returns and volatility between oil market and foreign exchange market. Ding and Vo (2012) use GARCH models to examine the volatility dependence between oil market and Foreign Exchange Market. In the pre-crisis period (before 2008), they find no interaction between the two markets. However, during the financial crisis, they show a bidirectional volatility interaction between the two markets. Recently, Truchis and Keddad (2015) conclude to a weak dependence between foreign exchange market and oil market. Our paper is related to the above studies. Accordingly, we propose to investigate volatility comovement between oil market and Euro/Dollar foreign exchange market. Our work differs 4

from the previous literature in several ways. Specifically, we use recent intraday data to investigate the instantaneous intraday linkage between the two markets. Moreover, in the best our knowledge, our paper is the first which investigate the spillover of extreme price changes (jumps) from the foreign market to the oil market. In fact, in the recent period US dollars have been significantly appreciated against Euro, and it will be interesting to investigate the impact of this appreciation on oil prices. Our intraday analysis reveals several results. First, we show that there is a volatility spillover from the foreign exchange market to the oil market. Second, intraday jumps occurred in the foreign market have a significant impact on oil market conditional volatility. Finally, we show that intraday jumps occur simultaneously in the Euro/Dollar foreign market and in the oil market, which validates the hypothesis of co-jump. The reminder of the paper is organised as fellows. Section 2 presents the data and the methodology. Results will be presented in section 3. Section 4 provides some concluding remarks.

2. Data and Methodology 2.1. Data The aim of this study is to examine intraday linkage between the Euro/Dollar exchange rate and the oil market. Intraday data is obtained from Bloomberg database and covers the period of five months from August, 2014 to January, 2015. During this period of study, we compute 5-minute returns for WTI index and for Euro/dollar exchange rate. Table 1 reported descriptive statistics concerning exchange rate and oil returns time series. We note…..

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2.2. Methodology 2.2.1. Intraday jump detection It is well-known that the logarithm price process can be expressed as a continuous-time jumpdiffusion model: dP(t ) = µ (t )dt + σ (t )dW (t ) + k (t )dq(t )

(1)

where: P(t) denotes the logarithmic asset price at time t, µ(t) is a continuous and locally bounded variation process, σ(t) denotes a strictly positive, right continuous and left limited stochastic volatility process, W(t) is a standard Brownian notion and q(t) refers to a pure jump process with intensity λ(t) and jump size κ(t). The usual quadratic variation of the cumulative return process is defined as t

QVt = ∫ δ ( s )ds + 2

0

Nt

∑k

2

( s)

(2)

0< s ≤t

Thus, the total variation of the price process (QVt) is composed of the continuous Brownian component and the sum of squared jumps. Andersen and Bollerslev (1998) proposed an estimator for the quadratic variation (QVt). This estimator called the realized variance (RV) is defined as the sum of intraday squared return. 1

RV t +1 ( ∆ ) ≡

∆

∑r j =1

2 t + j∆ , ∆

(3)

Barndorff-Nielsen and Shephard (2004) introduced the bipower variation (BV) as robust to jump estimator, defined as follows: 1

BVt +1 (∆) ≡ µ

−2 1

∆

∑r j=2

Where: µ1 = 2 π

t + j∆ , ∆

rt +( j −1) ∆ , ∆

(4)

(5)

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Instead of detecting the trading days that contain jumps, in this study we propose to identify intraday jumps. For that reason, we use the test proposed by Andersen et al. (2007)2. The authors test whether a randomly selected intraday return is subject to a jump: 1

∆

rt +ξ .∆ ,∆ = ∑ rt + j.∆ , ∆ ∐(ξ = j )

(6)

j =1

With ξ is an independently drawn index (uniformly distributed) from the set 1,2,...,1 / ∆ and rt + j.∆ ,∆ have conditional mean and variance given by Ert + j .∆ ,∆ and vrt + j .∆ , ∆ respectively.

The above return is considered as a jump by comparing its absolute value to corresponding scaled return realizations, which is distributed as follows: −1 / 2

∆

rt +ξ .∆ ,∆ → N (0, IVT +1 ).

(7)

Then, the multiple intraday jumps k s (∆) is detected based on the following rule:

[

]

k s (∆) = rt + s.∆ , ∆ . ∏ rt + s.∆ ,∆ . > φ1− β / 2 . ∆.BVt +1 (∆) , s = 1,2,...,1 / ∆

(8)

We choose the level α for the jump test at the daily frequency and we define the corresponding confidence interval ( 1 − β ) for intraday diffusive returns. With β = 1 − (1 − α ) ∆ and φ1− β / 2 is the appropriate critical value from the standard normal distribution.

2.2.2. GARCH model Formally, we applied the class of GARCH to check for volatility spillover between international stock markets. But rather than impose a certain model as in previous studies, we carried out different specifications, and the appropriate model was endogenously used

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We used also the test of Lee and Mykland (2008) and we have obtained similar results. We note that the only difference between these two tests is in their critical values.

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according to a battery of statistical tests. Operationally, we focused on further volatility transmission between the Euro-Dollar exchange market and oil market. The first step consists of measuring volatility, which we obtain using the GARCH specification proposed by Bollerslev (1986). We should recall that while the ARCH model by Engle (1982) implies that current idiosyncratic variance conditionally depends on past innovations, a GARCH model extends this specification through a parsimonious parameterization of the lag structure. The second step consists of testing for further spillover effects from a foreign market to the domestic market using the approach adopted by Hamao et al. (1990), Baur and Jung (2006) and Miralles-Marcelo et al. (2010). Accordingly, we introduce the most recent squared returns of the foreign exchange market in the conditional variance equation of the oil market. Moreover, lagged returns from the oil market and the foreign exchange market are introduced in the mean equation in order to capture further persistence and memory effects in the stock return dynamics. In this study, we propose using the TGARCH (Threshold General Auto Regressive Conditional Heteroskedasticity) model proposed by Zakoïan (1994) and Glosten et al. (1993). The use of a TGARCH model is appropriate for our study as it allows the sign and the magnitude of unanticipated excess returns to have separate effects on the volatility. Indeed, this model takes into account the asymmetric response of volatility to news. The asymmetric coefficient (γ) allows testing if negative shocks (Г=1 when ε0) of equal magnitude. We use a TGARCH (1,1) as this structure is sufficient to clean the autocorrelation of normalized residual series and squared standardized residuals (according to Q-statistics and ARCH-LM test presented in tables 2, 3, 4, 5 and). Thus, the TGARCH specification to test spillover effect from foreign exchange to oil crude market is written as:

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OILRt = µ 0 + a1OILRt −1 + a2 EXCHR t −1 + ε t

ε t = ν t ht , ν t → N (0,1)

(9)

ht2 = ω + α ε t2−1 + β ht2−1 + λ EXCHR t2−1 + γε t2−1Γt −1 where OILRt and OILRt −1 are the current and the lagged oil returns respectively; EXCHRt −1 and EXCHRt2−1 refer to the lagged Euro-Dollar returns and lagged squared EuroDollar returns respectively. The parameters µ 0 , ω , a i , ∀i = 1,7.α , β , λ , γ are the coefficients to be estimated. All returns are calculated using logarithm formula.

The TGARCH specification to test the impact of jumps occurred on foreign exchange on oil crude market conditional volatility is written as: OILRt = µ 0 + a1OILRt −1 + a2 EXCHR t −1 + ε t

ε t = ν t ht , ν t → N (0,1)

(10)

ht2 = ω + α ε t2−1 + β ht2−1 + λ EXCHJ t + γε t2−1Γt −1 where OILRt and OILRt −1 are the current and the lagged oil returns respectively; EXCHRt −1 and EXCHJ t refer to the lagged Euro-Dollar returns and the intensity of the current Euro-Dollar jump respectively. The parameters µ 0 , ω , a i , ∀i = 1,7.α , β , λ , γ are the coefficients to be estimated. All returns are calculated using logarithm formula.

Finally, we test the co-jump between the two markets. For that we run the following Tobit estimation and we introduce volume in the equation. If the variable σ 3 that means that jumps occurred simultaneously on the crude oil market and on the exchange rate market, which validates the co-jump hypothesis. 9

Jump_oilt= σ 1 + σ 2 Jump_exchanget-1 + σ 3 Jump_exchanget + σ 4 Oil_volumet

(11)

With: Jump_oilt: is the intensity the jump occurred on the crude oil market during the 5-minute interval t. Jump_exchanget: is the intensity the jump occurred on the exchange rate market during the 5minute interval t. Oil_volumet : is the logarithm trading volume on the crude oil market during the 5-minute interval t.

3. Results Table 2 recapitalizes the results of the estimation of model 1. It tests the volatility spillover from the Euro/Dollar exchange rate market to the oil market. The TGARCH estimation reveals the following results. First, crude oil returns depend on past oil returns and past exchange rate returns. This relation is negative which shows that an appreciation of US dollar leads to a decrease on oil prices. Second, regarding the variance equation, we show that the ARCH and the GARCH effects are significant.

However, we don’t find evidence of

asymmetric effect. In fact, the leverage coefficient is not significant. Finally, the coefficient of the Euro/Dollar squared returns is significant, which highlights evidence of volatility spillover from foreign exchange market to crude oil markets. Table 3 summarises the result of equation 2, which examine the impact of jumps occurred in Euro/Dollar exchange market on conditional volatility of crude oil market. These findings confirm the above results about the negative relation between Euro/Dollar returns and oil returns. Second, it confirms the significance of ARCH and GARCH coefficients. Finally, we show that the jumps occurred in the Euro/Dollar exchange market positively impact 10

conditional volatility of the oil market. That means that abrupt shocks occurred in the exchange rate markets are immediately transmitted to the oil market. To take the analysis further, we break down our sample into two sub-samples: jumps initiated by positive returns and jumps initiated by negative returns. Table 4 shows that the two types of jumps cause an increase of volatility of oil market. However, we notice an asymmetric reaction as the impact of positive shocks is higher than those of negative shocks. That means that dollar appreciation against Euro has a greater impact on crude oil prices (negative oil price returns) than dollar depreciation (positive oil price returns).

Table 5 reported results of model 5, which tests the co-jump hypothesis between crude oil market and the exchange rate market. These finding indicate that there is no link between past jumps and current jumps. That means that we can’t forecast jump in oil market from previous Euro/Dollar jumps. However, there is a contemporaneous relation between jumps in the exchange market and in the oil market, which highlights the evidence of co-jump between the two markets. Finally, we confirm the positive relation between volume and jumps.

4. Conclusion This paper aims at studying the relationship between crude oil market and euro/dollar exchange rate market. Our intraday analysis reveals several results. First, we confirm previous results which highlight volatility spillover from foreign exchange rate market to oil market. Second, we focus on abrupt (extreme) shocks and we show that jumps occurred in the exchange rate market impact volatility of the oil market. Furthermore, our results indicate that both positive and negative shocks impact the volatility. However, oil price reaction is greater in the case of an appreciation of the US dollar than in the case of a depreciation of the US currency. Finally, we find evidence of co-jump between the two markets as there is a 11

significant contemporaneous relation between the jumps occurred during each 5 minutes in both markets.

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Table 1: Descriptive statistics Table 2: Volatility Spillover from Euro/Dollar to oil market The significance at 10% level is marked by (*), 5% level by (**) and 1% level by (***). Q2( j ) are the LjungBox statistics of order j (j=12 or 24), respectively, for standardized residuals.

Coefficient

Estimation

P-value

Standard errors

Mean constant

-5.53E-06*

0.0685

3.04E-06

Rendt-1

-0.065770***

0.000

0.005988

RendEURDOLLt-1

-0.047577***

0.000

0.017281

Variance constant

1.04E-09***

0.007

3.90E-10

ARCH

0.1488***

0.000

0.00788

GARCH

0.864375***

0.000

0.003735

Leverage

0.0061

0.4951

0.009067

Squared SP&500t-1

0.233670***

0.000

0.020686

ARCH-LM test

0.694495

0.6769

12

24

36

7.7129

11.256

13.197

Ljung-Box statistics j Q2(j)

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Table 3: Impact of Euro/Dollar jumps on oil market conditional volatility The significance at 10% level is marked by (*), 5% level by (**) and 1% level by (***).Q2( j ) are the LjungBox statistics of order j (j=12 or 24), respectively, for standardized residuals.

Coefficient

Estimation

P-value

Standard errors

Mean constant

-5.37E-06*

0.0794

3.06E-06

Rendt-1

-0.065405***

0.000

0.006015

RendEURDOLLt-1

-0.045949***

0.0024

0.015131

Variance constant

3.43E-09***

0.000

4.21E-10

ARCH

0.164582***

0.000

0.008355

GARCH

0.865938***

0.000

0.003605

Leverage

0.007381

0.4338

0.009431

Squared SP&500t-1

0.000198***

0.000

4.06E-05

ARCH-LM test

1.016980

0.4166

Ljung-Box statistics j

12

24

36

Q2(j)

11.470

15.833

18.384

14

Table 4: Impact of positive and negative Euro/Dollar jumps on oil market conditional volatility The significance at 10% level is marked by (*), 5% level by (**) and 1% level by (***).Q2( j ) are the LjungBox statistics of order j (j=12 or 24), respectively, for standardized residuals.

Coefficient

Estimation

P-value

Standard errors

Mean constant

-5.35E-06*

0.0805

3.06E-06

Rendt-1

-0.065401***

0.000

0.006014

RendEURDOLLt-1

-0.045980***

0.0024

0.015130

Variance constant

3.42E-09***

0.000

4.21E-10

ARCH

0.164567***

0.000

0.008353

GARCH

0.865996***

0.000

0.003604

Leverage

0.007280

0.4400

0.009427

Pos.jump

0.000225***

0.000

5.95E-05

Neg.Jump

0.000165***

0.0069

6.11E-05

ARCH-LM test

1.018176

0.4158

Ljung-Box statistics

12

24

36

Q2(j)

11.483

15.850

18.404

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Table 5: Tobit model Tobit Model: Jump_oilt= σ 1 + σ 2 Jump_exchange,t-1 + σ 3 Jump_exchange,t + σ 4 Oil_volume,t

Dependent variable / independent variable

Estimation

P-value

Constant

-0.028608**

0.000

Jump_exchanget

1.320304**

0.0289

Jump_exchanget-1

-0.039696

0.9619

Oil_volume

2.49E-06***

0.000

Log likelihood

122.6837

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References

Andersen, T., Bollerslev, T., 1998. Deutsche markedollar volatility: intraday volatility patterns, macroeconomic announcements and longer run dependencies. The Journal of Finance 1, 219-265. Andersen, T. G., Bollerslev, T., Dobrev, D., 2007. No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications. Journal of Econometrics 138, 125-180. Akram, Q.F., 2009. Commodity prices, interest rates and the dollar. Energy Economy 31, 838–851. Barndorff-Nielsen O.E., Shephard N., 2004. Power and bipower variation with stochastic volatility and jumps, Journal of Financial Econometrics 2, 1-37. Beckmann, J., Czudaj, R., 2013. Is there a homogeneous causality pattern between oil prices and currencies of oil importers and exporters? Energy Economics 40, 665–678. Bénassy-Quéré, A.,Mignon, V., Penot, A., 2007. China and the relationship between the oil price and the dollar. Energy Policy 35, 5795–5805. Ding, L., Vo, M., 2012. Exchange rates and oil prices: a multivariate stochastic volatility analysis. Quantitative Review of Economic and Finance 52, 15–37. Jammazi, R., Lahiani, A. and Nguyen, D.K. 2015. A wavelet-based nonlinear ARDL model for assessing the exchange rate pass-through to crude oil prices. Journal of International Financial Markets, Institutions & Money 34, pp.173–187. Lee, S.S., Mykland, P.A., 2008. Jumps in financial markets: A new nonparametric test and jump dynamics. Review of Financial Studies 21, 2535-2563. Reboredo, J.C., Rivera-Castro, M.A., 2013. A wavelet decomposition approach to crude oil price and exchange rate dependence. Economic Modelling 32, 42–57. Salisu, A.A., Mobolaji, H., 2013. Modeling returns and volatility transmission between oil price and US–Nigeria exchange rate. Energy Economy 39, 169–176. Tantatape, B., Huang, J.C and Sissoko, Y. 2014. Crude oil prices and exchange rates: Causality, variance decomposition and impulse response. Energy Economics, Vol. 44, pp.407– 412. Yousefi, A., Wirjanto, T.S., 2004. The empirical role of the exchange rate on the crude-oil price formation. Energy Economy 26, 783–799. 17

Zhang, Y.-J., Fan, Y., Tsai, H.-T.,Wei, Y.-M., 2008. Spillover effect of US dollar exchange rate on oil prices. Journal of Policy Modelling 30, 973–999.

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