Related papers: A simple microstructure return model explaining mi…
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…
We present two statistical causes for the distortion of correlations on high-frequency financial data. We demonstrate that the asynchrony of trades as well as the decimalization of stock prices has a large impact on the decline of the…
A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a…
We demonstrate that the lowest possible price change (tick-size) has a large impact on the structure of financial return distributions. It induces a microstructure as well as it can alter the tail behavior. On small return intervals, the…
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…
We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that…
We analyse the dependence of stock return cross-correlations on the sampling frequency of the data known as the Epps effect: For high resolution data the cross-correlations are significantly smaller than their asymptotic value as observed…
The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…
Time and the choice of measurement time scales is fundamental to how we choose to represent information and data in finance. This choice implies both the units and the aggregation scales for the resulting statistical measurables used to…
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet…
We introduce a new model for describing the fluctuations of a tick-by-tick single asset price. Our model is based on Markov renewal processes. We consider a point process associated to the timestamps of the price jumps, and marks associated…
It is a well-documented fact that the correlation function of the returns on two "related" assets is generally increasing as a function of the horizon $h$ of these returns. This phenomenon, termed the Epps Effect, holds true in a wide…
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…
In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or…
The Epps effect, the decrease of correlations between stock returns for short time windows, was traced back to the trading asynchronicity and to the occasional lead-lag relation between the prices. We study pairs of stocks where the latter…
We present a method to compensate statistical errors in the calculation of correlations on asynchronous time series. The method is based on the assumption of an underlying time series. We set up a model and apply it to financial data to…
We present a novel microscopic stock market model consisting of a large number of random agents modeling traders in a market. Each agent is characterized by a set of parameters that serve to make iterated predictions of two successive…
We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the…
We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise…
Equity options are known to be notoriously difficult to price accurately, and even with the development of established mathematical models there are many assumptions that must be made about the underlying processes driving market movements.…