Related papers: Multifactor Analysis of Multiscaling in Volatility…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some…
The probability distribution of log-returns for financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of…
We conclude from an analysis of high resolution NYSE data that the distribution of the traded value $f_i$ (or volume) has a finite variance $\sigma_i$ for the very large majority of stocks $i$, and the distribution itself is non-universal…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
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,…
We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_\gamma$…
We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of…
Income and risk coexist, yet investors are often so focused on chasing high returns that they overlook the potential risks that can lead to high losses. Therefore, risk forecasting and risk control is the cornerstone of investment. To…
We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…
We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
In practice daily volatility of portfolio returns is transformed to longer holding periods by multiplying by the square-root of time which assumes that returns are not serially correlated. Under this assumption this procedure of scaling can…
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the…
Investigations of inverse statistics (a concept borrowed from turbulence) in stock markets, exemplified with filtered Dow Jones Industrial Average, S&P 500, and NASDAQ, have uncovered a novel stylized fact that the distribution of exit time…
With the increasing volume of high-frequency data in the information age, both challenges and opportunities arise in the prediction of stock volatility. On one hand, the outcome of prediction using tradition method combining stock technical…
The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and…
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…