We analyse the dependence of stock return cross-correlations on the data sampling frequency, known as the Epps effect: for high-resolution data the cross-correlations are significantly smaller than their asymptotic value as observed for daily data. The former description implies that a changing...

Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modelling the power-law tails of the returns distribution in terms of a Student-t...

We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility...

We consider different levels of complexity which are observed in the empirical investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time series are rather complex under several ways. Specifically, they are...

We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities...

We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal...

We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Δ, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled orders in a double auction market. We find that the distribution of all...

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of nine improved covariance estimation procedures using daily returns of 90 highly...

We investigate the time series of the degree of minimum spanning trees (MSTs) obtained by using a correlation-based clustering procedure which starts from (i) asset return and (ii) volatility time series. The MST is obtained at different times by computing correlation among time series over a...