An empirical analysis on euro hungarian forint exchange rate volatility using garch

An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 40 AN EMPIRICAL ANALYSIS ON EURO HUNGARIAN FORINT EXCHANGE RATE VOLATILITY USING GARCH Ngo Thai Hung1 1Corvinus University of Budapest, Hungary Information: Received: 18/04/2017 Accepted: 24/05/2017 Published: 06/2017 Keywords: Volatility, GARCH, EURHUF, Volatility forecast ABSTRACT The paper aims to analyse and forecast the Euro Hungarian Forint exchange rate volatility with the use of generalized autoregressive conditional heteroscedasticity GARCH- type models over the time period from September 30, 2010 to January 02, 2017. This model is the extension of the ARCH process with various features to explain the obvious characteristics of financial time series such as asymmetric and leverage effect. As we apply EUR/HUB with this model, the estimation and forecast are performed. 1. INTRODUCTION During recent years, the study of the volatility of a market variable measuring uncertainty about the future value of the variable plays a prominent part in monitoring and assessing potential losses. Quantitative methods measure the volatility of the Euro Hungarian Forint exchange rate received the high interest because of its role in determining the price of securities and risk management. Typically, a series of financial indices have different movements under certain period. This means that the variance of the range of financial indicators changes over time. The Euro Hungarian Forint exchange rate is one of the most crucial markets by market capitalization and liquidity in central Europe. According to Econotimes (2016): “the momentum of Hungarian economic growth is likely to slow in 2016, following a strong expansion of 3 percent last year. The Hungarian economy will be impacted by the warning of the regional auto industry boom, pausing of EU fund inflow in 2016 before picking up again in 2017 and the risk to the German economy from developments in China. The end of easing cycle is expected to result in a stable forint in the coming quarters. However, the currency is likely to face slight upward pressure from Brexit related uncertainties. The EUR/HUF is likely to trade at 322 by the end of 2016, stated Commerzbank. Persistent low inflation is expected to renew rate cut expectations in the coming year. Such a development, combined with an expected deceleration of the GDP growth in 2016, is expected to exert upward pressure on the EUR/HUF pair by the end of 2016”. Therefore, the investigation of the volatility of the Euro Hungarian Forint exchange rate is in need. As Bantwa (2017) mentioned, for most investors, the prevailing market turmoil and a lack of clarity on where it's headed are a cause for concern. The majority of investors in markets are mainly concerned about the uncertainty in getting the expected returns as well as the volatility in returns. Andersen T. and Labys (2003) provided a framework for integrating high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Use of realized volatility computed from high-frequency intraday An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 41 returns permits used of traditional time series methods for modeling and calculating. Ashok and Ritesh (2011) center on comparing the performance of conditional volatility model GARCH and Volatility Index in predicting underlying volatility of the NIFTY 50 index. Using high-frequency data the underlying volatility of NIFTY50 index is captured. Several approaches to predicting realized volatility are considered. Chatayan Wiphatthanananthakul (2010) estimated ARMA-GARCH, EGARCH, GJR and PGARCH models for Thailand Volatility Index (TVIX), and made comparison and forecast between the models. GARCH model has become key tools in the analysis of time series data, particularly in financial applications. This model is especially useful when the goal of the study is to analyze and forecast volatility Degiannakis (2004). With the generation of GARCH models, it is able to reproduce another very vital stylized fact, which is volatility clustering; that is, big shocks are followed by big shocks. In this paper, we applied GARCH model to estimate, compute and forecast the EUR/HUF volatility. Nevertheless, it should be pointed out that several empirical studies have already examined the impact of asymmetries on the performance of GARCH models. The recent survey by Poon and Granger (2003) provides, among other things, an interesting and extensive synopsis of them. Indeed, different conclusions have been drawn from these studies. The rest of the paper proceeds as follows: the concept of volatility and GARCH model are given in next section, the final section is discussed results and conclusion. 2. Theoretical Background, Concept and Definitions 2.1 Definition and Concept of Volatility C.Hull (2015) stated that “the volatility  of a variable is defined as the standard deviation of the return provided by the variable per unit of time when the return is expressed using continuous compounding. When volatility is used for option pricing, the unit of time is usually one year, so that volatility is the standard deviation of the continuously compounded return per year. However, when volatility is used for risk management, the unit of time is usually one day, so that volatility is the standard deviation of the continuously compounded return per day. In general, T is equal to the standard deviation of 0 ln T S S       where TS is the value of the market variable at time T and 0S is its value today. The expression 0 ln T S S       equals the total return earned in time T expressed with continuous compounding. If  is per day, T is measured in days, if  is per year, T is measured in years”. The volatility of EUR/HUF variable is estimated using historical data. The returns of EUR/HUF at time t are calculated as follows: 1 ln , 1,ii i p R i n p    where ip and 1ip  are the prices of EUR/HUF at time t and t-1, respectively. The usual estimates s of the standard deviation of the iR is given by 2 1 1 ( ) 1 n i i s R R n      where R is the mean of the iR . As explained above, the standard deviation of the iR is T where  is the volatility of the EUR/HUF. The variable s is, therefore, an estimate of T . It follows that  itself can be estimated as ˆ , where ˆ s T   An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 42 The standard error of this estimate can be shown to be approximate ˆ 2n  . T is measured in days, the volatility that is calculated is a daily volatility. 2.2 GARCH Model GARCH model by Bollerslev(1986) imposes important limitations, not to capture a positive or negative sign of tu , which both positive and negative shocks have the same impact on the conditional variance, th , as follows t t tu   2 2 2 1 1 1 p q t i t j t j i j u            where 0  , 1 0  , for 1,i p and 0j  for 1,j q are sufficient to ensure that the conditional variance, t is nonnegative. For the GARCH process to be defined, it is required that 0  . Additionally, a univariate GARCH(1,1) model is known as ARCH( ) model Engle, (1982) as an infinite expansion in 2 1tu  . The  represents the ARCH effect and  represents the GARCH effect. GARCH(1,1) model, 2t is calculated from a long run average variance rate, LV , as well as from 1t  and 1tu  . The equation for GARCH(1,1) is 2 2 2 1 1t L t tV u       where  is the weight assigned to LV ,  is the weight assigned to 2 1tu  and  is the weight assigned to 2 1t  . Since the weight must sum to one, we have 1     2.3 Volatility forecasting There is a broad and relatively new theoretical approach that attempts to compare the accuracies of different models for conducting out-of-sample volatility forecasts. Akgiray (1989) observed the GARCH model superior to ARCH, exponentially weighted moving average and historical mean models for forecasting monthly US stock index volatility. West and Cho (1995) indicated that the apparent superiority of GARCH used one-step-ahead forecasts of dollar exchange rate volatility, although for longer horizons, the model behaves no better than their alternatives. Specifically, Day and Lewis (1992) examined in depth and considered the out-of-sample forecasting performance of GARCH and EGARCH models for predicting the volatility of stock index. Arowolo, W.B (2013) concluded that the Optimal values of p and q GARCH (p,q) model depends on location, the types of the data and model order selected techniques being used. The models that Day and Lewis employ so called a ‘plain vanilla’ GARCH(1,1): 2 0 1 1 1 1t t th u h      when he applied the properties of linear GARCH model for daily closing stocks prices of Zenith bank PlC in Nigeria stocks Exchange 2.4 Data Description The data for our empirical investigation consists of the EUR/HUF index transaction prices that is obtained from Bloomberg, accounted by the Department of Finance, Corvinus University of Budapest, the sample period is from September 30, 2010 to January 02, 2017 which constitutes a total of n = 1654 trading days. For the estimation, we use the daily returns of EUR/HUF to estimate GARCH(1,1) by using Eview 7.0 software. 3. RESULTS 3.1 Descriptive Statistics The descriptive statistics of daily logarithmic returns of the EUR/HUF is given in Table 1. An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 43 Table 1. Descriptive statistics of EUR/HUF Returns Mean Std. Dev Skewness Kurtosis Max Min 0.000068 0.005235 0.087168 4.479947 0.022156 -0.021550 Jarque-Bera 153.0389 Probability 0.000000 Source: Author’s calculation The average return of EUR/HUF is positive. A variable has a normal distribution if its skewness statistic equals to zero and kurtosis statistic is 3, but the return of EUR/HUF has positive skewness statistic and high kurtosis, suggesting the presence of fat tails and a non-symmetric series. Additionally, as we can see from Jarque-Bera normality test rejects the null hypothesis of normality for the sample, this means we can draw a conclusion that the return of EUR/HUF is not normally distributed. The relatively large kurtosis indicates non-normality that the distribution of returns is leptokurtic. Figure 1 depicts the histogram of daily logarithmic return for EUR/HUF. From this histogram, it appears that EUR/HUF returns have high peak than the normal distribution. In general, Q-Q plot is used to identify the distribution of the sample in the study, it compares the distribution with the normal distribution and indicates that EUR/HUF returns deviate from the normal distribution. Figure 1. Histogram and Q-Q Plot of Daily Logarithmic EURHUF returns Figure 2 presents the plot of price and EUR/HUF returns. This indicates some circumstances where EUR/HUF returns fluctuate. An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 44 Figure 2. Daily price and EURHUF returns The unit root tests for EUR/HUF returns are summarized in Table 2. The Augmented Dickey- Fuller (ADF) and Phillips-Perron (PP) tests were used to test the null hypothesis of a unit root against the alternative hypothesis of stationarity. The tests have large negative values of statistics in all cases for levels such that the return variable rejects the null hypothesis at the 1 per cent significance level, therefore, the returns are stationary. Table 2. Unit root test for Returns of EUR/HUF Test None Constant Const & Trend Phillips-Perron -43.07319 -43.07511 -43.06830 ADF -42.82135 -42.81734 -42.80833 Source: Author’s calculation 3.2 Estimation Table 3 represents the ARCH and GARCH effects from statistically significant at 1 percent level of  and  . It shows that the long-run coefficients are all statistically significant in the variance equation. The coefficient of  appears to show the presence of volatility clustering in the models. Conditional volatility for the models tends to rise (fall) when the absolute value of the standardized residuals is larger (smaller). The coefficients of  (a determinant of the degree of persistence) for all models are less than 1 showing persistent volatility. 260 270 280 290 300 310 320 330 2010 2011 2012 2013 2014 2015 2016 PRICE -.03 -.02 -.01 .00 .01 .02 .03 2010 2011 2012 2013 2014 2015 2016 LN_RETURN An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 45 Table 3. GARCH on Returns of EUR/HUF GARCH Mean Equation Variance Equation Coefficient z-statistics Coefficient z-statistics Constant 0.000022 0.205460  0.000000163 2.468227 (0.0136) Mean  0.054850 6.529890 (0.0000)  0.938494 101.6264 (0.0000) Source: Author’s calculation GARCH(1,1) model is estimated from daily data as follows 2 2 2 1 1 0.000000163 0.054850 0.938494 t t t u       Since 1     , it follows that 0,000656  and, since LV  . We have 0,000024489LV  . In other words, the long run average variance per day implied by the model is 0,000024489. This corresponds to a volatility of 0,000024489 0.004948 or 0,49 %, per day. 3.3 Forecasting Results Using GARCH (1,1) Model The selected model 2 2 2 1 1 0.000000163 0.054850 0.938494 t t t u       has been tested for diagnostic checking and there is no doubt of its accuracy for forecasting based on residual tests. We can use our model to predict the future volatility value. Figures 3 and 4 show the forecast value. It is seen that the forecast of the conditional variance indicates a gradual decrease in the volatility of the stock returns. The dynamic forecasts show a completely flat forecast structure for the mean, while at the end of the in-sample estimation period, the value of the conditional variance was at a historically lower level relative to its unconditional average. Therefore, the forecast converges upon their long term mean value from below as the forecast horizon decreases. Notice also that there are no  2-standard error band confidence intervals for the conditional variance forecasts. It is evidence for, static forecasts that the variance forecasts gradually fall over the out–of sample period, they show much more volatility than for the dynamic forecasts. An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 46 Figure 3. Static forecasts of the conditional variance Figure 4. Dynamic forecasts of the conditional variance 4. CONCLUSION This paper estimates the volatility of the Euro Hungarian Forint exchange rate returns using GARCH model from the seemingly complicated volatility formula established by Bollerslev (1986). The results of statistical properties obtained supported the claim that the financial data are leptokurtic. The GARCH model was identified to be the most appropriate for the time-varying volatility of the data. The results from an empirical analysis based on the Euro Hungarian Forint exchange rate showed the volatility is 0.49 % per day. Additionally, the results of forecasting conditional variance indicate a gradual decrease in the volatility of the stock returns. This is in contrast to the work of Chatayan Wiphatthanananthakul (2010). REFERENCES Ashok Bantwa. (2017). A study on India volatility index (VIX) and its performance as risk management tool in Indian Stock Market. Indian Journal of Research. 06:248, 251. Akgiray, V. (1989) Conditional Heteroskedasticity in Time Series of Stock Returns: Evidence and Forecasts, Journal of Business. 62(1), 55—80. Arowolo, W.B. (2013), Predicting Stock Prices Returns Using GARCH Model, The International Journal of Engineering and Science. 2, 32-37. Banerjee Ashok & Kumar Ritesh. (2011). Realized Volatility and India VIX, IIM Calcutta. Working Paper Series. (688). Chatayan Wiphatthanananthakul & Songsak Sriboonchitta (2010), The Comparison among - GARCH, -EGARCH, -GJR, and -PGARCH An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 47 models on Thailand Volatility Index, The Thailand Econometrics Society. 2(2), 140 – 148. Diebold F.X. Andersen T., Bollerslev T., & P. Labys. (2003). Modelling and Forecasting Realized Volatility. Econometrica. 71:529, 626. Day, T. E. & Lewis, C. M. (1992) Stock Market Volatility and the Information Content of Stock Index Options, Journal of Econometrics. 52, 267—87. Econotimes. (2016). Hungarian economic growth to slow in 2016; EUR/HUF likely to face mild upward pressure. Retrieved from economic-growth-to-slow-in-2016-EUR-HUF- likely-to-face-mild-upward-pressure-232142. John C.Hull. (2015). Risk management and Financial Institutions. John Wiley & Sons, Inc., Hoboken, New Jersey. Stavros Degiannakis. (2004). 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An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 48 APPENDIX The residual test Date: 03/17/17 Time: 14:57 Sample: 10/01/2010 2/01/2017 Included observations: 1654 Autocorrelation Partial Correlation AC PAC Q-Stat Prob | | | | 1 -0.027 -0.027 1.2230 0.269 | | | | 2 -0.008 -0.008 1.3206 0.517 | | | | 3 -0.063 -0.064 7.9102 0.048 | | | | 4 -0.016 -0.019 8.3203 0.081 | | | | 5 -0.008 -0.010 8.4150 0.135 | | | | 6 0.017 0.013 8.9164 0.178 | | | | 7 -0.013 -0.015 9.2126 0.238 | | | | 8 0.034 0.032 11.090 0.197 | | | | 9 -0.011 -0.008 11.307 0.255 | | | | 10 -0.033 -0.035 13.170 0.214 | | | | 11 0.017 0.019 13.632 0.254 | | | | 12 -0.011 -0.012 13.846 0.311 | | | | 13 0.017 0.013 14.318 0.352 | | | | 14 0.017 0.018 14.816 0.391 | | | | 15 -0.043 -0.042 17.849 0.271 | | | | 16 -0.063 -0.065 24.568 0.078 | | | | 17 -0.036 -0.040 26.762 0.062 | | | | 18 0.013 0.008 27.066 0.078 | | | | 19 0.011 -0.000 27.286 0.098 | | | | 20 -0.012 -0.019 27.511 0.121 | | | | 21 0.019 0.020 28.145 0.136 | | | | 22 -0.009 -0.009 28.274 0.167 | | | | 23 -0.031 -0.030 29.922 0.152 | | | | 24 0.018 0.021 30.476 0.169 | | | | 25 -0.039 -0.041 32.992 0.131 | | | | 26 -0.024 -0.034 33.958 0.136 An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 49 | | | | 27 0.014 0.010 34.281 0.158 | | | | 28 -0.024 -0.026 35.216 0.164 | | | | 29 0.010 0.005 35.399 0.192 | | | | 30 0.000 0.000 35.399 0.228 | | | | 31 0.009 0.006 35.523 0.264 | | | | 32 0.003 -0.008 35.537 0.305 | | | | 33 0.037 0.034 37.850 0.257 | | | | 34 0.000 0.008 37.850 0.298 | | | | 35 0.019 0.013 38.475 0.315 | | | | 36 -0.045 -0.037 41.892 0.230 Heteroskedasticity Test: ARCH F-statistic 0.815876 Prob. F(1,1651) 0.3665 Obs*R-squared 0.816461 Prob. Chi-Square(1) 0.3662 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 03/17/17 Time: 14:59 Sample (adjusted): 10/04/2010 2/01/2017 Included observations: 1653 after adjustments 0 40 80 120 160 200 240 -3 -2 -1 0 1 2 3 4 Series: Standardized Residuals Sample 10/01/2010 2/01/2017 Observations 1654 Mean 0.015260 Median -0.032466 Maximum 4.447776 Minimum -3.232094 Std. Dev. 0.998667 Skewness 0.169411 Kurtosis 3.492414 Jarque-Bera 24.62201 Probability 0.000005 An Giang University Journal of Science – 2017, Vol. 5 (2), 40 – 50 50 Variable Coefficient Std. Error t-Statistic Prob. C 0.974711 0.045924 21.22463 0.0000 WGT_RESID^2(-1) 0.022225 0.024606 0.903258 0.3665 R-squared 0.000494 Mean dependent var 0.996877 Adjusted R-squared -0.000111 S.D. dependent var 1.578091 S.E. of regression 1.578178 Akaike info criterion 3.751629 Sum squared resid 4112.059 Schwarz criterion 3.758175 Log likelihood -3098.721 Hannan-Quinn criter. 3.754056 F-statistic 0.815876 Durbin-Watson stat 2.000105 Prob(F-statistic) 0.366521