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Academy of Economic Studies Doctoral School of Finance and Banking HEAT WAVES VERSUS METEOR SHOWERS An Analysis of Volatility Spillovers in the Romanian Exchange Market. Msc.Student James Omoto Anyanzwa

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slide1

Academy of Economic Studies Doctoral School of Finance and BankingHEAT WAVES VERSUS METEOR SHOWERS An Analysis of Volatility Spillovers in the Romanian Exchange Market

Msc.Student James Omoto Anyanzwa

Supervisor Professor Moisăr Altăr

Bucharest, July 2007

contents
CONTENTS
  • Importance of cross-market volatility spillovers
  • The objectives of the paper
  • Empirical Studies
  • Data
  • Model
  • Conclusions
  • References
importance of cross market volatility spillovers
Importance of Cross-Market volatility Spillovers
  • Volatility can be defined as the risk associated with the ownership of a financial asset over a given holding period. It refers to the rate at which the price of a financial asset change over time, and it is measured either through the standard deviation or variance of the asset return (Taylor 2005)
  • An important interpretation of spillovers is that of information linkage across markets i.e. the reaction of a market to the arrival of new information revealed in the other exchange markets.
  • The new information/news is reflected in price changes in a market
  • Volatility spillovers occurs mostly when economies are related through trade and investment (Engle et al 1994,Cappiello,Gerard, ,and Manganeli 2004) i.e. any news about economic fundamentals in one country will most likely have an implication for the other country.

Why study Volatility Spillovers?

  • Important for pricing of securities within and across markets, international diversification strategies, hedging strategies and for regulatory policy.
  • Important in evaluating regulatory proposals in order to restrict international capital flows (Chan and Hooy 2003).
the objectives of the paper
The Objectives of the Paper
  • To investigate and test two volatility theories:
  • Whether exchange rate volatility in Romania is purely determined by domestic factors, which is consistent with Heat Wave Hypothesis
  • Whether exchange rate volatility in Romania is also influenced by foreign factors such as exchange rate changes in the Eurozone, which is consistent with the Meteor Showers hypothesis.
  • Whether there exist any asymmetric response of the Romanian exchange market to foreign shocks.
  • Whether there is any volatility spillovers out of Romania.
empirical studies on volatility spillovers
Empirical Studies on Volatility Spillovers
  • Previous studies concentrated mostly on volatility spillovers in international equity markets e.g.Mervyn and Wadhwani (1990), Hamao, Masulis, and Ng (1990),Lin,Engle,and Ito (1994),King,Sentana,and Wadhwani(1994). All these studies find evidence of cross-border correlation of stock markets and volatility spillovers.

Edwards(1998) uses augmented GARCH model to analyze possibility of interest rate spillovers from Mexico to Argentina and Chile.The results indicate significant spillovers into Argentina and not Chile.

  • Lau and Ivaschenko (2002) examine price and volatility spillovers in the Tech and non-Tech sectors in the US and the Asian countries.

The following studies focus on volatility spillovers in exchange markets:

  • Engle,Ito,and Lin (1990),Bailie and Bollerslev (1990),

Recently there has been renewed interest to investigate volatility spillovers in the exchange markets of emerging and transition economies. Among these studies include;

  • Habib (2002)-uses GARCH model to investigate impact of external factors on daily exchange rates and interest rates in Hungary, Czech Republic and Poland.
slide6
Kocenda (2005)-uses the GARCH model to study the exchange rate behavior of the Czech crown which is pegged to a currency basket with an imposed narrow band.
  • Pramor and Tamirisa (2006)-studies convergence between the CEECs and Eurozone by use of GARCH methodology
  • Karacadag(2004)-analyses the effect on intervention on the level and volatility of the exchange rate in Mexico and Turkey
  • Horvàth(2005)-uses a simple “out-of-sample” approach to predict exchange rate volatility for several CEECs based on Optimum Currency Area (OCA)criterion.

In all these studies the authors find evidence of volatility spillovers across markets using GARCH model or its extensions.

slide7
DATA

-

--Initial data series: Nominal daily exchange rates for Romanian RON/USD,Eurozone EUR/USD, Bulgarian Lev/USD,Hungarian forint/USD and Croatian Kuna/USD.

- Time length: 1:06:2003-12:29:2006,

- A total of 1004 observations for each exchange rate series, after adjusting for missing values.

- All the data series are converted into the same currency, the US dollar

- The data series were collected from the websites of each country’s central bank.

- On July 1,2005 Romania introduced new currency the Ron i.e. 1RON=10,000 ROL,hence the ROL data series was converted to RON to ensure uniformity.

-ADF Test showed all the data series were non-stationary and integrated of order one,hence FIRST Differencing could make them stationary.

-Modified form: First Differences of Logarithms of RON/USD (dlogRON/USD),EUR/USD (dlogEUR/USD), Lev/USD(dlogBGN/USD), Forint/USD(dlogHUF/USD) and Kuna/USD (dlogHRK/USD) exchange rates.

slide8

Evolution of Exchange rates against the US Dollar:Nominal values Exists evidence of different degrees of volatility in the emerging Europe and the Eurozone.Countries with highly flexible exchange rate regime such as Eurozone are more volatile, compared to those with Comparatively rigid Regimes (Kocenda and Valachy 2005).

the model
The Model
  • Most popularly used tools for modeling volatility in financial times series are:

-Autoregressive Conditional Heteroskedasticity (ARCH) model, Engle (1982)

-Generalized ARCH (GARCH) model,Bollerslev (1986)

Why ARCH/GARCH Models?

  • These models can capture the non-linear dependence (heteroskedasticity) inherent in financial time series data i.e. the autocorrelation of absolute or squared returns.
  • Financial returns including exchange rates are known to exhibit the stylized facts attributed to Mandelbrot (1963)i.e. (1) their distributions are Leptokurtic (2)Non- constant variance (3) volatility clustering.

These facts are only appealing in the context of high frequency data such as exchange rates.

garch 1 1 model
GARCH (1,1) Model
  • Thesimplest GARCH (1,1) model is given as :

(i)

(ii)

  • The model consist of two components: Mean equation (i) and Variance equation (ii) for the financial asset return. In our case,

is the exchange rate change over two consecutive trading days, is the number of lags chosen by a certain lag selection criteria under the condition of stationarity e.g. the absolute values of must be less than a unit ,the error term, is assumed to be a white noise i.e. mean zero, and independent over time (no serial correlation between the error terms).

conditions for stationarity
Conditions for Stationarity
  • However with financial asset returns, though disturbance terms are serially uncorrelated, they are not independent i.e. they are heteroskedastic.
  • The constraints ensures that conditional variance is always positive.
  • While the condition 0 < <1 ensures a positive autocorrelation in the volatility process, ,and measures volatility persistence with a rate of decay governed by ( D1+D2).The closer the sum of DI and D2 is to one the slower the rate at which shocks on conditional variance in the next period dies out. This sum must also be less than one to ensure that the GARCH(1,1) model is stationary.
  • The upper limit of D1+D2=1,is the case of an integrated process.
  • The GARCH(1,1) model implies that the current volatility is an exponentially weighted moving average of past squared returns.
  • The model is estimated by maximization of the likelihood functions because of its non-linearity.i.e iteration procedures.
  • Stationary GARCH(1,1) model has dynamics that produces reversions of the short run conditional volatility to a constant long run or unconditional variance given as:
model specification for the romanian case
Model Specification for the Romanian Case:
  • We base our analysis on the work done by Engle,Ito,and Lin (1990), with slight modifications on the original model.
  • Contrary to previous work by Engle’ et al , we use daily exchange rate data and eliminate the influence of current foreign volatility on Romanian conditional variance equation.
  • We use notations RON/USD,EUR/USD,BGN/USD,HUF/USD, and HRK/USD to denote Romanian,Eurozone,Bulgarian,Hungarian and Croatian exchange rates against the US Dollar respectively.
  • All exchange rate series are expressed in the US Dollar in order to allow correlations in the disturbance terms.
  • Exchange markets are labeled as 1 for Romania,2 (Eurozone), 3 (bulgaria),4 (Hungary) and 5 (croatia)
  • Our model is thus based on the following assumptions:

- that the RON/USD volatility is time-varying ,being a function of its own past values (realizations), past endogenous squared residuals, and past cross-market squared volatility changes.

continuation
Continuation:
  • Our sample size, consists of 5 exchange markets i.e. Romania RON/USD) ,Eurozone (EUR/USD), Bulgaria (BGN/USD),Hungary (HUF/USD),and Croatia( HRK/USD)

We denote the Exchange rate change (return) in market at time as and given as:

for

The time-scale is one day ( in our case), though it may vary between a minute or even seconds for tick data. Observations “z” are sampled at discrete times

Time lags is denoted by

Each exchange rate return ( ) is assumed to be normally distributed with mean zero ,but with a non-constant variance ( ).

The conditional volatility in market is thus described as :

slide15

Evidence of Heteroskedasticity (non-constant variance) in exchange rate returns. Large returns follow large returns (of either sign) and small returns follow small returns (of either sign) i.e. volatility clustering.

interpretation
interpretation
  • The distribution of all the exchange rate returns are positively skewed (except for Romania), have average returns close to 0,and show evidence of fat tails i.e. they are leptokurtic (kurtosis value greater than 3)

Hence the exchange rate return series show evidence of the “stylized facts “associated with all financial return series.

GARCH(1,1) Test,AR(1) Vs MA(1) Tests

  • The return series were tested for GARCH effects by use of Engle (1982) Lagrange Multiplier(LM) Test. The null hypothesis of homoskedasticty was rejected, implying presence of heteroskedasticity. The GARCH(1,1) effects was tested based on ARCH(2) as proposed by Bollerslev (1986:318) i.e for an ARCH(q) null,the LM test for GARCH(r,q) and ARCH(q+r) coincide,hence a positive test for ARCH(2) could be an indicative of GARCH(1,1) process.
slide17
Using the Autocorrelation and Partial Autocorrelation functions i.e. ACF and PCF,it was discovered that all the exchange rate return series could best be described by a Moving Average process of order one –MA(1).
  • It means the current value of each return series depends on its past error terms but not on its previous values in which case it would be an autoregressive process of order one-AR(1)
  • Decision rule:

An AR(p) process has a declining ACF and the PACF is zero for lags greater than p.

An MA(q) process has a ACF that is zero for lags greater than q and PACF that declines exponentially.

The mean equation for each exchange market is thus an MA(1) process.

model
model:
  • for= 1,2,3….. and = 1,2,3….. for
  • Where and stands for domestic and foreign markets
  • respectively. is the information set available on market on date
  • The set contains last period’s information about changes in fundamentals from market and market
  • is the distribution of , while is the conditional variance for market on date
  • is assumed to be normally distributed with mean 0 and non-constant variance The conditional variance is viewed as being a function of its own past values ( ) , endogenous squared residuals( ) and squared residuals from foreign markets ( )
interpretation of model coefficients
Interpretation of model coefficients
  • The cross-market volatility spillover coefficient is given by
  • The coefficient for is consistent with null hypothesis of Heat Waves effect . It means no volatility spillovers i.e. conditional volatility( ) in market is only determined purely by its own previous values and endogenous squared residuals ( )
  • When the coefficient is significantly different from zero for

it means presence of Meteor Showers i.e. conditional volatility in market

is also influenced by volatilities in foreign markets ( )

The significance of and implies presence of both Heat Waves and Meteor Showers effects.

The conditional volatility model for each exchange market is given as:

Estimated results are shown in Table 1.

Model was estimated by use of Bernd,Hall,Hall,and Hausman (1974) (BHHH) algorithms in E-Views 4.0 software.

slide20

Table 1 MA(1)-GARCH(1,1) Daily HEAT WAVE ESTIMATION RESULTSWhere implying Romania,Eurozone,Bulgaria,Hungary and Croatian markets respectively

discussion of results
Discussion of Results
  • Theresults shows a strong GARCH Effect for all the market segments. Estimated coefficients in the GARCH term are positive and significant in all the markets indicating a powerful influence of own volatility on the current volatility.
  • The coefficients indicate presence of Heat Wave effects in all the markets i.e. conditional volatility in each market is determined by internal factors.
  • The values in parentheses represents the standard errors for each estimated coefficient.
  • Furthermore ,in line with stationarity conditions we find that
  • Hence GARCH(1,1) stability conditions are satisfied.
cross market volatility spillovers
Cross-Market Volatility Spillovers
  • After inclusion of squared residuals/innovations from foreign markets as additional regressors in the RON/USD BGN/USD,HUF/USD and HRK/USD conditional variance equations. the following equations were estimated:
  • The results are presented in Table 2
table 2 ma 1 garch 1 1 daily meteor showers estimation results
Table 2 MA(1)-GARCH(1,1) Daily Meteor Showers Estimation Results
slide25
NOTES: RONMVt-1, EUMVt-1, BGNMVt-1, HRKMVt-1 stands for one lagged period volatilities in the Romanian, European Union, Bulgarian ,Hungarian and Croatian markets respectively
  • Discussion of Results
  • The results indicates that in addition to own volatility, the conditional volatility in each of the CEEC markets is influenced by news/innovations coming from at least one of the four other markets.
  • The model coefficients satisfy the GARCH requirement that

and

All coefficients in the Romanian variance equation are significant i.e It means both Heat Waves and Meteor Showers are present. The RON/USD exchange rate volatility ( ) is determined by its own past volatility ( )

slide26
And also by exchange rate changes in the foreign markets i.e. Eurozone

( ),Bulgaria ( ),Hungary ( ),and Croatia ( )

The Eurozone has the largest spillover volatility coefficient (0.040479).It means exchange rate changes in the Eurozone has greater impact on the RON/USD volatility, compared to Bulgaria, Hungary and Croatian volatilities which have negative spillover coefficients.

However the most powerful determinant of RON/USD volatility is its own previous volatility. The spillover coefficient for Romanian volatility is negative in Bulgarian and Croatian exchange markets and positive in Hungarian exchange markets. This shows insignificant spillovers from Romania into Bulgaria and Croatia and significant spillovers into Hungary.

ma 1 tarch 1 1 model
MA(1)-TARCH(1,1) Model
  • We employ the Threshold GARCH (1,1) model of Glosten,Jagannathan,and Runkle (1993) in order to capture any asymmetry in the foreign shocks impacting on Romanian RON/USD volatility. The model incorporates a leverage term that allows for the asymmetric effects of good and bad news. A similar approach was used by Savva,Osborn and Gill(2005) to examine asymmeric volatility spillovers and correlations between the US and European Stock markets(New York,London,Franfurt and Paris Stock markets).
  • Hence drawing on the work by Savva et al (2005) we introduce a multiplicative dummy as an indicator function to check for any statistical difference in the event of negative shocks.
daily heat waves ma 1 tarch 1 1 model specification
Daily Heat Waves MA(1)- TARCH(1,1) model Specification
  • Cross-market TARCH(1,1) model
  • Where and are domestic and foreign markets respectively.
  • is the multiplicative dummy variable. It assumes the value of one in the case of negative shocks (i.e ) and zero in the case of a positive shock (i.e )

so good and bad news have different effects.

  • Spillovers are captured by the coefficient for
interpretation of coefficients
Interpretation of coefficients

The size and direction of the shock is determined by the coefficient

The coefficient is negative in the case of asymmetry ,implying bad news/innovation has greater impact on conditional volatility than good new/innovations.

Therefore a statistically positive , coupled with a negative (positive)

Implies that negative innovations in market have a greater impact on volatility of market than positive (negative) innovations. The positive value of coefficient indicates a decreased conditional variance i.e. no asymmetry and vice versa.

slide30

Table 3 Heat WavesMA(1)-TARCH(1,1) Conditional Variance Estimation Results.

slide31
For implying Romanian,Eurozone, ,Bulgarian,Hungarian and Croatian markets respectively.
  • is the Leverage term(indicator function) in the TARCH(1,1) model.
  • The coefficient is positive for all the markets except Bulgaria,meaning no asymmetry in domestic shocks affecting Romanian,Eurozone,Hungarian and Croatian market volatilities.it means both good and bad news/innovations have the same effect on conditional volatilities. The coefficient in the case of Bulgarian market indicting presence of asymmetry i.e bad news/innovations has greater impact on Bulgarian conditional volatility than good news.
cross market ma 1 tgarch 1 1 for romania exchange market
Cross-market MA(1)-TGARCH(1,1) for Romania Exchange Market
  • A cross-market TGARCH(1,1) was estimated for the Romanian exchange market. To determine the nature of each foreign shock, different shocks were incorporated into the Romanian conditional variance equation one at a time because introducing all the shocks into the equation makes it impossible to determine the asymmetry of each shock.
  • For 1,2,3,4,5 imply Romanian,Eurozone,Bulgarian,Hungarian and Croatian markets respectively.
slide33
Romanian Cross-market MA(1)-TARCH(1,1) Estimation Results
  • Where Eurozone,Bulgaria,Hungary and Croatian markets
discussion of estimated results
Discussion of Estimated Results
  • The results shows that volatility transmission mechanism for the Eurozone and Bulgarian exchange markets is asymmetric i.e. the coefficients measuring asymmetry is signficant for the two markets,reinforcing the assertion that bad news increases volatility more than the good news.
  • Thus a negative innovation in the Eurozone and Bulgarian markets is estimated to increase volatility in the Romanian market by 0.093502 and 0.038191times respectively than that of a positive innovation of the same magnitude.
  • The coefficient is positive in the case of Hungarian and Croatian shocks i.e both good and bad news/innovations from these markets have the same impact on the Romanian RON/USD volatility.
conclusion
Conclusion
  • In this paper we used interdaily nominal exchange rate data to analyze volatility spillovers into the Romanian exchange market from the Eurozone and a group of selected CEECs exchange markets. The analysis was based on two alternative GARCH (1, 1) and TARCH (1, 1) specifications. The symmetric GARCH approach assumes that the impact of a shock on conditional volatility is the same, regardless of whether the shock is positive or negative. Alternatively, the TARCH model takes into account the asymmetric effects, and assumes that the impact of a shock on conditional volatility is not the same but it is determined by the sign of the shock.
  • Using the two approaches, we estimated the conditional variance for each exchange rate return series and tested for cross-market volatility spillovers. Our main interest was to find whether exchange rate changes in foreign markets have any significant influence on the Romanian RON/USD volatility and whether leverage effects are present.
  • First we tested each exchange rate return series for ARCH effects using Engle’s Lagrange Multiplier (LM) Test, and then implemented an identification test using Autocorrelation and Partial autocorrelation functions to determine the structure for each return series. All the return series (RON/USD,EURO/USD,BGN/USD,HUF/USD and HRK/USD) were found to contain GARCH(1,1) effects and were best described by the moving average process of order one i.e MA(1).
slide36
Our findings provide support for the presence of both Heat Waves and Meteor Showers on the Romanian Exchange market. It means Romanian RON/USD volatility is determined both by its own previous volatility (i.e. Heat Wave hypothesis) and by exchange rate changes in foreign markets (i.e. Meteor Showers hypothesis).These findings also indicate that the RON/USD volatility responds asymmetrically to news from some selected markets. In particular, we find that news/innovations from the Eurozone market has a significant influence on the RON/USD volatility, and they are also highly asymmetric. This means bad/negative news from the Eurozone exchange market has a larger impact on Romanian RON/USD volatility than the good/positive news.
  • Our findings also indicate that the impact of exchange rate changes in Bulgaria, Hungary and Croatia on the Romanian RON/USD volatility is insignificant. With the exception of Bulgaria, we find that news/innovations from these CEECs markets, though insignificant, are highly symmetric, implying both bad and good news will have the same impact on the RON/USD volatility. However our results indicate that the Heat Wave hypothesis is very powerful in determing the RON/USD volatility than the Meteor Showers. It means Romanian RON/USD volatility is determined mostly by its own previous values than external factors.
slide37
Our results conforms to Pramor and Tamirisa (2006) findings that volatility transmits from developed to emerging markets, and that smaller, less developed markets are likely to be more sensitive to transmitted shocks. These findings are important to investors in formulation of trading strategies, risk management and to monetary authorities especially in the formulation of monetary policies. It is also important for Romanian policy makers to understand the sources of volatility in the exchange market particularly as the country hopes to join the European Exchange rate management mechanism 11 (ERM11) in a bid to adopt the euro as its official currency sometimes in the future. Our study was restricted to determining the sources of volatility shocks; however questions related to the main causes of volatility shocks remain an area of further research.
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