Related papers: Activity spectrum from waiting-time distribution
This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the…
In this paper, a new approach to bivariate modeling of autoregressive conditional duration (ACD) models is proposed. Specifically, we consider the joint modeling of durations and the number of transactions made during the spell. The…
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance.…
We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent…
Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading,…
We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and…
The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has…
We consider the response of a finite string to white noise and obtain the exact time-dependent spectrum. The complete exact solution is obtained, that is, both the transient and steady-state solution. To define the time-varying spectrum we…
In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly…
For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a-, b-, and c-increments. Statistics of the a-b-c-increments are computed for the Time & Sales…
We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level…
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…
High-speed computerized trading, often called "high-frequency trading" (HFT), has increased dramatically in financial markets over the last decade. In the US and Europe, it now accounts for nearly one-half of all trades. Although evidence…
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the…
In most real scenarios the construction of a risk-neutral portfolio must be performed in discrete time and with transaction costs. Two human imposed constraints are the risk-aversion and the profit maximization, which together define a…
We study the behavior of simple models for financial markets with widely spread frequency either in the trading activity of agents or in the occurrence of basic events. The generic picture of a phase transition between information efficient…
In this article, we first provide a taxonomy of dynamic spectrum access. We then focus on opportunistic spectrum access, the overlay approach under the hierarchical access model of dynamic spectrum access. we aim to provide an overview of…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
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.…
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an…