Return-volatility correlation in financial dynamics

Abstract

We investigate the return-volatility correlation both local and nonlocal in time with daily and minutely data of the German DAX and Chinese indices, and observe a leverage effect for the German DAX, while an antileverage effect for the Chinese indices. In the negative time direction, i.e., for the volatility-return correlation, an antileverage effect nonlocal in time is detected for both the German DAX and Chinese indices, although the duplicate local in time does not exist. A retarded volatility model may describe the asymmetric properties of the financial indices in the positive time direction.

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“…On the other hand, L(t) for the Shanghai Index remains positive for about 10 days. That is the so-called anti-leverage effect [6,55]. The return-volatility correlation function produced in the model is in agreement with that calculated from empirical data on amplitude and duration for both the S&P 500 and Shanghai indices.…”

“…∆R is computed from the linear relation between ∆r and ∆R for all these indices. days, and this is the well-known leverage effect [61,1,6]. On the other hand, L(t) for the Shanghai Index remains positive for about 10 days.…”

“…The negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics [1,6,55,56]. Although various macroscopic models have been proposed to describe the return-volatility correlation, it is very important to understand the correlations from the microscopic level.…”

“…The interactions of multiple agents induce various collective phenomena, such as the abnormal distributions, temporal correlations, and sector structures [1,2,3,4,5,6,7,8,9]. The complex financial systems are also substantially influenced by the external information that may, for example, drive the systems to non-stationary states, larger fluctuations or extreme events [10,11,12,13,14,15,16,17].…”

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“…Besides biomedical (Ashkenazy et al, 2001;Kantelhardt et al, 2002) or hydrological (Livina et al, 2003) applications, the evaluation of volatility correlations is widely used in econometric time series (Liu et al, 1999;Qiu et al, 2006). It has been recognized quite a time that the magnitudes of price changes exhibit long-range correlations, reflecting the fact that economic markets experience quiet periods with clusters of less pronounced price fluctuations, followed by more volatile periods with pronounced jumps up and down.…”