Related papers: A Stochastic Feedback Model for Volatility
We study, both analytically and numerically, an ARCH-like, multiscale model of volatility, which assumes that the volatility is governed by the observed past price changes on different time scales. With a power-law distribution of time…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made,…
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times…
We present a model of financial markets originally proposed for a turbulent flow, as a dynamic basis of its intermittent behavior. Time evolution of the price change is assumed to be described by Brownian motion in a power-law potential,…
In this paper we explain the wild fluctuations of financial prices from the intrinsic amplifying feedback of speculative supply and demand. Formally, we show that an asset return follows a multiplicative random growth with exogenous input,…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…