Related papers: Hitting Time Distributions in Financial Markets
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
Financial markets exhibit alternating periods of rising and falling prices. Stock traders seeking to make profitable investment decisions have to account for those trends, where the goal is to accurately predict switches from bullish…
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk…
In this paper we present a continuous time dynamical model of heterogeneous agents interacting in a financial market where transactions are cleared by a market maker. The market is composed of fundamentalist, trend following and contrarian…
A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked…
The correlated stochastic volatility models constitute a natural extension of the Black and Scholes-Merton framework: here the volatility is not a constant, but a stochastic process correlated with the price log-return one. At present,…
The correlation coefficient between stocks depends on price history and includes information on hierarchical structure in financial markets. It is useful for portfolio selection and estimation of risk. I introduce the Life Time of…
This study conducts a comprehensive analysis of time series segmentation on the Japanese stock prices listed on the first section of the Tokyo Stock Exchange during the period from 4 January 2000 to 30 January 2012. A recursive segmentation…
We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the…
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model…
A non-Bayesian time-varying model is developed by introducing the concept of the degree of market efficiency that varies over time. This model may be seen as a reflection of the idea that continuous technological progress alters the trading…
The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend.…
Using the most comprehensive source of commercially available data on the US National Market System, we analyze all quotes and trades associated with Dow 30 stocks in 2016 from the vantage point of a single and fixed frame of reference. We…
Equity default-swaps pay the holder a fixed amount of money when the underlying spot level touches a (far-down) barrier during the life of the instrument. While most pricing models give reasonable results when the barrier lies within the…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Predicting the intraday stock jumps is a significant but challenging problem in finance. Due to the instantaneity and imperceptibility characteristics of intraday stock jumps, relevant studies on their predictability remain limited. This…
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option…
An empirical study of joint bivariate probability distribution of two consecutive price increments for a set of stocks at time scales ranging from one minute to thirty minutes reveals asymmetric structures with respect to the axes y=0, y=x,…