Statistical Finance
We investigate topology and temporal evolution of the foreign currency exchange market viewed from a weighted network perspective. Based on exchange rates for a set of 46 currencies (including precious metals), we construct different…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
We review the decomposition method of stock return cross-correlations, presented previously for studying the dependence of the correlation coefficient on the resolution of data (Epps effect). Through a toy model of random walk/Brownian…
The statistical properties of the return intervals $\tau_q$ between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold $q$ are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks…
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in…
We investigate the probability distribution of the return intervals $\tau$ between successive 1-min volatilities of two Chinese indices exceeding a certain threshold $q$. The Kolmogorov-Smirnov (KS) tests show that the two indices exhibit…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the…
The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now…
In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce…
First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations…
The purpose of this paper is to study the generalized Fong--Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as…
A linear link between S&P 500 return and the change rate of the number of nine-year-olds in the USA has been found. The return is represented by a sum of monthly returns during previous twelve months. The change rate of the specific age…
An algorithm based on Renormalization Group (RG) to analyze time series forecasting was proposed in cond-mat/0110285. In this paper we explicitly code and test it. We choose in particular some financial time series (stocks, indexes and…
The paper is devoted to elaboration of a novel specific indicator based on the modified Holder exponents. This indicator has been used for forecasting critical points of financial time series and crashes of the USA stock market. The…
We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space;…
In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are…
We study the relation between serial correlation of financial returns and volatility at intraday level for the S&P500 stock index. At daily and weekly level, serial correlation and volatility are known to be negatively correlated (LeBaron…
One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known…
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…