We examine whether the relationship between market volatility and network properties in the low-frequency level can be applied to the high-frequency level. For the analysis, we use the minimum spanning tree (MST) method constructed from intraday Korean stock market data. The results show that the higher the market volatility is, the denser the MST of stocks becomes. The normalized tree length shows a strong negative relationship with market volatility, indicating that the distances between nodes are shorter when the market volatility is high. The mean occupation layer shows the tendency of having a smaller value in a higher volatility market. The maximum number of links becomes larger when the market volatility increases. All these network properties support the network being dense and shrinking in high market volatility conditions; that is, the degree of co-movement in financial market is reinforced in the intraday high-frequency level.
The topological perspective on financial markets has received much attention in the field of econophysics [1], [2], [3], [4], [5], [6], [7], [8] and [9]. A financial market itself is generally considered as a complex system, tangled intricately. Mantegna [4] proposed the transformation of correlation coefficients to the Euclidean distance. The correlation coefficient is calculated from log return of two assets. A lot of research has attempted to apply the minimum spanning tree (MST) method to various financial areas: stock markets (global [10] and [11], developed market [1], [2], [9], [12], [13], [14], [15], [16] and [17], emerging market [3], [18] and [19]), interest rates [20] and [21], currencies [22], [23] and [24], bonds [25], and commodities [26]. Most of this research is static analysis, such as overviews on the network topology or taxonomic studies in terms of sector, region, or other characteristics. Recently, Coelho et al. [11] attempted a dynamic analysis. Onnela et al. [5] provided the basic idea that the market condition is reflected in the topology of networks in a financial market by comparing the topological difference between Black Monday and a day of normal conditions. Gilmore et al. [25] studied the dynamic co-movement of government bonds in 1998–2006 using hierarchical tree and network properties. Jang et al. [22] showed that the topology of a currency network is changed in a currency crisis. However, these studies did not cover intraday level analysis. On the other hand, the importance of high-frequency intraday analysis of the financial market has been gradually highlighted as the investment time horizon gets shorter thanks to the advances of computing and communication technologies. Accordingly, the interest in volatility is moving from daily toward intraday level [27], [28] and [29].
Our study focuses on the intraday high-frequency level analysis in the topology of a financial network. Assets are actively traded in a short time horizon and the number of assets traded during the short time period is sufficient to construct a network structure. Considering these conditions, we analyze a stock market in which trading is executed in an automated electronic system. By this analysis, we try to extend the previous research to intraday level analysis and to find a more generalized relationship between the volatility of the financial market and the corresponding network properties.
This paper is organized as follows. The following section gives a brief description of the data and provides some preliminary analysis including intraday stylized facts. Section 3 reports our findings on the network properties for various market volatility levels. Finally, a summary and conclusions are presented.
We investigated the relationship between the market volatility and the network properties of the MST in the intraday high-frequency level dynamics using intraday Korean stock market data.
The results suggest that the network structure becomes denser as the market volatility increases. The NTL responds negatively to the market volatility, so the trend of the NTL series is a reverse image of that of the market volatility series. The MOL tends to decreases as the market volatility increases, and View the MathML sourcekmax shows the tendency of increasing for higher market volatility.
All these network properties consistently support the characteristics observed from the analysis of low-frequency dynamics (daily or longer) also being found in the intraday high-frequency dynamics. In other words, as a market becomes volatile, the co-movement tendency of financial assets is reinforced at the intraday high-frequency level in a similar way to or longer low-frequency level.
