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The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…
Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a…
We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our…
We propose a simple stochastic model of market behavior. Dividing market participants into two groups: trend-followers and fundamentalists, we derive the general form of a stochastic equation of market dynamics. The model has two…
This paper conducts an extensive analysis of Bitcoin return series, with a primary focus on three volatility metrics: historical volatility (calculated as the sample standard deviation), forecasted volatility (derived from GARCH-type…
We propose that the minimal requirements for a model of stock market price fluctuations should comprise time asymmetry, robustness with respect to connectivity between agents, ``bounded rationality'' and a probabilistic description. We also…
This paper investigates the time-varying risk-premium relation of the Chinese stock markets within the framework of cross-sectional momentum and contrarian effects by adopting the Capital Asset Pricing Model and the French-Fama three factor…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
Price without transaction makes no sense. Trading volume authenticates its corresponding price, so there exist mutual information and correlation between price and trading volume. We are curious about fractal features of this correlation…
We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times…
This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The…
The relationship between price volatilty and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the…
Prediction markets are often described as mechanisms that ``aggregate information'' into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and…
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be…
In this paper we study the asymptotic behavior of a Boltzmann type price formation model, which describes the trading dynamics in a financial market. In many of these markets trading happens at high frequencies and low transactions costs.…
One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…
We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility)…
We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices…
We study the dynamics of order flows around large intraday price changes using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a significant reversal of price for both intraday price decreases and increases with a…