Volatility Cluster and Herding

Stock markets can be characterized by fat tails in the volatility distribution, clustering of volatilities and slow decay of their time correlations. For an explanation models with several mechanisms and consequently many parameters as the Lux-Marchesi model have been used. We show that a simple herding model with only four parameters leads to a quantitative description of the data. As a new type of data we describe the volatility cluster by the waiting time distribution, which can be used successfully to distinguish between different models.Comment: 15 pages TeX, 6 figures PostScrip

Semi-parametric estimation of joint large movements of risky assets

The classical approach to modelling the occurrence of joint large movements of asset returns is to assume multivariate normality for the distribution of asset returns. This implies independence between large returns. However, it is now recognised by both academics and practitioners that large movements of assets returns do not occur independently. This fact encourages the modelling joint large movements of asset returns as non-normal, a non trivial task mainly due to the natural scarcity of such extreme events. This paper shows how to estimate the probability of joint large movements of asset prices using a semi-parametric approach borrowed from extreme value theory (EVT). It helps to understand the contribution of individual assets to large portfolio losses in terms of joint large movements. The advantages of this approach are that it does not require the assumption of a specific parametric form for the dependence structure of the joint large movements, avoiding the model misspecification; it addresses specifically the scarcity of data which is a problem for the reliable fitting of fully parametric models; and it is applicable to portfolios of many assets: there is no dimension explosion. The paper includes an empirical analysis of international equity data showing how to implement semi-parametric EVT modelling and how to exploit its strengths to help understand the probability of joint large movements. We estimate the probability of joint large losses in a portfolio composed of the FTSE 100, Nikkei 250 and S&P 500 indices. Each of the index returns is found to be heavy tailed. The S&P 500 index has a much stronger effect on large portfolio losses than the FTSE 100, although having similar univariate tail heaviness

Analysis of the intraday effects of economic releases on the currency market

Using four years of second-by-second executed trade data, we study the intraday effects of a representative group of scheduled economic releases on three exchange rates: EUR/$, JPY/$ and GBP/$. Using wavelets to analyze volatility behavior, we empirically show that intraday volatility clusters increase as we approach the time of the releases, and decay exponentially after the releases. Moreover, we compare our results with the results of a poll that we conducted of economists and traders. Finally, we propose a wavelet volatility estimator which is not only more efficient than a range estimator that is commonly used in empirical studies, but also captures the market dynamics as accurately as a range estimator. Our approach has practical value in high-frequency algorithmic trading, as well as electronic market making. --Foreign exchange,volatility estimation,economic release,wavelet,high frequency

Application of Zhangs Square Root Law and Herding to Financial Markets

We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is equivalent to the so called 3/2-model of stochastic volatility. The description of the unconditional distribution for the absolute returns is in good agreement with the DAX independent whether one uses the square root or a conventional linear relation. Only the statistic of extreme events prefers the former. The description of the autocorrelations are in much better agreement for the square root law. The volatility clusters are described by a scaling law for the distribution of returns conditional to the value at the previous day in good agreement with the data.Comment: 25 pages, 3 figures, Late

Tick size and price diffusion

A tick size is the smallest increment of a security price. It is clear that at the shortest time scale on which individual orders are placed the tick size has a major role which affects where limit orders can be placed, the bid-ask spread, etc. This is the realm of market microstructure and there is a vast literature on the role of tick size on market microstructure. However, tick size can also affect price properties at longer time scales, and relatively less is known about the effect of tick size on the statistical properties of prices. The present paper is divided in two parts. In the first we review the effect of tick size change on the market microstructure and the diffusion properties of prices. The second part presents original results obtained by investigating the tick size changes occurring at the New York Stock Exchange (NYSE). We show that tick size change has three effects on price diffusion. First, as already shown in the literature, tick size affects price return distribution at an aggregate time scale. Second, reducing the tick size typically leads to an increase of volatility clustering. We give a possible mechanistic explanation for this effect, but clearly more investigation is needed to understand the origin of this relation. Third, we explicitly show that the ability of the subordination hypothesis in explaining fat tails of returns and volatility clustering is strongly dependent on tick size. While for large tick sizes the subordination hypothesis has significant explanatory power, for small tick sizes we show that subordination is not the main driver of these two important stylized facts of financial market.Comment: To be published in the "Proceedings of Econophys-Kolkata V International Workshop on "Econophysics of Order-driven Markets" March 9-13, 2010, The New Economic Windows series of Springer-Verlag Italia

Role of Noise in a Market Model with Stochastic Volatility

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.Comment: 13 pages, 6 figures, Eur. Phys. J. B, in pres