Related papers: The Random Walk behind Volatility Clustering
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
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…
While the investors' responses to price changes and their price forecasts are well accepted major factors contributing to large price fluctuations in financial markets, our study shows that investors' heterogeneous and dynamic risk aversion…
We take a look the changes of different asset prices over variable periods, using both traditional and spectral methods, and discover universality phenomena which hold (in some cases) across asset classes.
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures.…
Standard economic theory assumes that agents in markets behave rationally. However, the observation of extremely large fluctuations in the price of financial assets that are not correlated to changes in their fundamental value, as well as…
In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous "square-root law" of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the…
We study the cause of large fluctuations in prices in the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price…
"Noise-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical…
We consider the randomness of market trade as the origin of price and return stochasticity. We look at time series of trade values and volumes as random variables during the averaging interval {\Delta} and describe the dependences of…
The influence of the past price behaviour on the realized volatility is investigated in the present article. The results show that trending (drifting) prices lead to increased (decreased) realized volatility. This ``volatility induced by…
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…
Having reliable estimates of the occurrence rates of extreme events is highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period,…
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws…
We show that time-dependent fluctuations $\{\Delta x\}$ in foreign exchange rates are accurately described by a random walk in a complex plane that is demarcated into the gain (+) and loss (-) sectors. $\{\Delta x\}$ is the outcome of $N$…
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
We propose a new volatility model based on two stylized facts of the volatility in the stock market: clustering and leverage effect. We calibrate our model parameters, in the leading order, with 77 years Dow Jones Industrial Average data.…
The analysis of financial markets using models inspired by statistical physics offers a fruitful approach to understand collective and extreme phenomena [3, 14, 15] In this paper, we present a study based on a 2D Ising network model where…
Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…