جهش های قیمتی در بازارهای سهام کشور Visegrad: تجزیه و تحلیل تجربی

We employ high frequency data to study extreme price changes (i.e., price jumps) in the Prague, Warsaw, Budapest, and Frankfurt stock market indexes from June 2003 to December 2010. We use the price jump index and normalized returns to analyze the distribution of extreme returns. The comparison of jump distributions across different frequencies, periods, up and down moves, and markets suggests a possible relationship with different market regulation and micro-structure. We also show that the recent financial crisis resulted in an overall increase in volatility; however, this was not translated into an increase in the absolute number of jumps.

The volatility of financial markets has been a deeply studied phenomenon in the financial literature for more than a century (see, e.g., the original work of Bachelier in Bachelier et al., 2006, or the recent survey of Gatheral, 2006). There exists an enormous stream in the literature that directly separates volatility into two parts: the noise and irregular and extreme price movements known as price jumps. See Merton (1976) for an early reference or the recent discussion of how to decompose volatility by Giot et al. (2010). However, most of the attention has so far been focused on the part of volatility known as regular noise, which can be described by a standard Gaussian distribution. The volatility of real assets, however, does not follow a simple Gaussian motion and the true volatility dynamics is more complex. (There is a wide range of technical literature devoted to non-Gaussian price-generating models, for example based on chaos theory, see the survey in Chorafas, 1994, based on fractal Brownian motion, see the introductory paper of Mandelbrot and Van Ness, 1968, or models with positive feedback, see Lin et al., 2009. In the recent literature, price jumps attract more attention despite the fact that they are difficult to explicitly define or handle mathematically (Broadie and Jain, 2008, Johannes, 2004, Nietert, 2001 and Pan, 2002). Price jumps can be connected to important issues in market micro-structure, such as the efficiency of price formation, the provision of liquidity or the interaction between market players, as can be seen in Madhavan (2000). From a practical point of view, traders and portfolio managers are also interested in analyzing price jumps since they are a part of volatility and therefore associated with potential big losses and gains. Moreover, one see interesting applications of price jumps distributions for financial engineers computing appropriate risk measures, including modified value at risk. Thus, understanding price jumps helps to avoid big losses, improves portfolio performance and better hedges positions. Finally, knowledge of price jumps is needed by financial regulators; see Becketti and Roberts (1990), Tiniç, (1995), Beirne et al. (2010), and Li and Rose (2009). In this paper, we empirically estimate a broad range of price jump properties for the main stock indexes of the Central and Eastern European (CEE) emerging markets. For our analysis we employ a discrete-time framework, which is suitable for markets with low and irregular frequency of trades. In particular, we are interested in measuring to what extent the jumpiness of the selected CEE markets has been affected by the recent financial crisis and how price jump indexes depend on a chosen frequency, as well as analyzing the (a)symmetry of the underlying jump distribution. In such a setup, the exact prediction of a price jump is not the primary concern, rather we want to compare the propensity of indexes to jump using a non-parametric framework. We use high-frequency (five-minute) data on the CEE stock market indexes covering the Czech Republic, Poland, and Hungary. These countries belong to the Visegrad region—small emerging economies regionally and culturally close to each other.1 An analogous country setup was used by Jayasuriya (2011), who studied the effect of the Chinese market on its emerging market neighbors. In our country group we employed the German DAX index from the Frankfurt stock exchange as a benchmark for two main reasons. First, Germany is by far the most important foreign trade partner for all CEE firms, and second, the German stock market is geographically the closest mature market and a very good proxy for Eurozone financial markets. The data spans from June 2003 to the end of 2010 and thus covers the period before the recent financial crisis, the phase before the crisis, as well as part of the recovery phase. To our knowledge, this is the first study of price jumps for small emerging markets that includes economic and financial interference and discusses the impact of a financial crisis on extreme price movements. Moreover, it is the first study suggesting comparisons of jump propensities across markets and time periods. The rest of the paper is structured as follows. Section 2 gives a short overview and classification of various price jump indicators. Section 3 briefly describes our methodology, in particular how we use non-parametric measures to compare stock market jumpiness across time and markets. Section 4 describes the data, Section 5 is devoted to our results, and finally Section 6 concludes the paper.

We performed an extensive analysis of price jumps using high-frequency data (5-, 10-, 15-, and 30-minute frequencies) for three emerging stock market indexes (PX, BUX, and WIG20) from the CEE Visegrad region. As a benchmark representing a geographically close and mature EU market we use the German DAX index. The time period of the data is from June 2003 to December 2010. For our analysis we employed two different indicators of price jumps: the price jump index and normalized returns. The analysis of returns revealed that the data substantially deviates from a Gaussian distribution and tends to support the presence of price jumps. We also analyze if we would observe larger negative extreme price movements compared to positive ones. However, the reverse is true and the intuitive asymmetry favoring negative price jumps does not hold, moreover, this result was robustly confirmed by both indicators. Further, the Prague Stock Exchange differs with respect to the presence of price jumps when lower frequencies are used. Based on the theory, one would assume that the lower the frequency, the more price jumps will be observed. However, the PX index reveals almost the opposite behavior, so the behavior of the PX index significantly differs from the remaining three market indexes. One can speculate that this difference could be explained by the composition of the PX index: a small number of components, a relatively high number (and weight) of stocks with dual trading, prices determined in other exchanges, and some components not being traded with high-frequency. Simply, a relatively small number of trades with a few stocks could have a large impact on the entire PX index. These explanations, however, would need additional analysis and the market micro-structure perspective should be tested across the markets, which is beyond the scope of this study. We have estimated the price jump properties quarter by quarter. This allows us to compare the estimated characteristic coefficients across stock market indexes and over time. We have thus employed quarterly estimates and the Wilcoxon test and show that there is no significant difference in the distributions of the characteristic coefficients moving up with respect to those moving down. Further, we have answered the question whether the price-generating process, or its price jump component, differs for all stock market indexes. The results of the Kruskal–Wallis test used with quarterly estimates suggest a deviation among the indexes for high-frequency returns. A detailed pair-wise comparison using the Wilcoxon test revealed that it is the PX index that causes the disagreement and the results thus further support the presence of a PX Puzzle. Another pattern, consistent across all frequencies, both jump price indexes, and up and down moves shows that PX was clearly the most jumpy index while WIG had the smallest propensity to jump. This calls for further research, suggesting a link between market micro-structure and jump propensity. In particular, higher market volatility and also higher propensity to jump is explained by differences in the population of investors (Prague is dominated by foreign investors, while Warsaw is dominated by strong domestic institutional investors, namely pension funds), differences in the regulatory framework in Prague, where there are much weaker margin regulatory requirements, and much higher leverage possibilities in Prague. Finally, we tested for the stability of the price jump component in time in particular during the recent financial crisis. The statistical tests suggest that the price jump component is stable before and during the financial crisis, although there are few cases when the processes were different. These disagreements occurred especially for high-frequency data. Overall, we cast light on the issue of extreme price movements and their distributions in CEE emerging markets. The quantitative understanding of price jumps can obviously help to decrease the risk connected with irregular but abrupt price changes and can be used to develop various financial models by computing associated risk measures. The empirical analysis presented in this study can also serve as a starting point for a larger study of the integration of financial markets, including the role of market micro-structure and the regulation of price jumps.