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Standard quantitative models of the stock market predict a log-normal distribution for stock returns (Bachelier 1900, Osborne 1959), but it is recognised (Fama 1965) that empirical data, in comparison with a Gaussian, exhibit leptokurtosis…
The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
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…
In this paper, we are interested in continuous time models in which the index level induces some feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the log-returns of each stock may be decomposed…
The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50…
The autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents. Such a case admits an explicit analytical solution of the problem of constructing the best linear forecast of a…
The daily volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well long-term trends. We also model the transition to a Gaussian distribution for longer time…
A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays $\tau$. The scale dependent behaviour of financial data can be divided into two regions.…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
The use of factor stochastic volatility models requires choosing the number of latent factors used to describe the dynamics of the financial returns process; however, empirical evidence suggests that the number and makeup of pertinent…
Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for…
We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous"…
This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of…
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be…
A few characteristic exponents describing power law behaviors of roughness, coherence and persistence in stochastic time series are compared to each other. Relevant techniques for analyzing such time series are recalled in order to…
Accurate forecasting of volatility and return quantiles is essential for evaluating financial tail risks such as value-at-risk and expected shortfall. This study proposes an extension of the traditional stochastic volatility model, termed…
Monitoring downside risk and upside risk to the key macroeconomic indicators is critical for effective policymaking aimed at maintaining economic stability. In this paper I propose a parametric framework for modelling and forecasting…
Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…
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…