Related papers: A Note on Jump Atlas Models
I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting…
We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of…
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on…
During a stock market peak the price of a given stock ($ i $) jumps from an initial level $ p_1(i) $ to a peak level $ p_2(i) $ before falling back to a bottom level $ p_3(i) $. The ratios $ A(i) = p_2(i)/p_1(i) $ and $ B(i)= p_3(i)/p_1(i)…
Providing a measure of market risk is an important issue for investors and financial institutions. However, the existing models for this purpose are per definition symmetric. The current paper introduces an asymmetric capital asset pricing…
This analysis derives the maximum likelihood estimator and applies Bayesian inference to model geometric Brownian motion, incorporating jump diffusion to account for sudden market shifts. The Bayesian approach is implemented using Markov…
We propose in this paper to consider the stock market as a physical system assimilate to a fluid evolving in a macroscopic space subject to a Force that influences its movement over time where this last is arising from the collision between…
We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…
A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which…
This paper continues a series of studies devoted to analysis of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response) at intraday timescales for a group of stocks. Besides the asymmetry…
Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
Large and stable indices of the world wide stock markets such as NYSE and SP 500 together with NASDAQ -- the index representing markets of new trends, and WIG -- the index of the local stock market of Eastern Europe, are considered. Due to…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market…
The present paper describes a practical example in which the probability distribution of the prices of a stock market blue chip is calculated as the wave function of a quantum particle confined in a potential well. This model may naturally…
We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock markets dynamics within an economic model based on simple temporal demand and supply functions [J. Phys. A: Math. Gen. 33, 3637…
A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is…
We introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. Our model is tested against financial datasets, showing an extremely good agreement…
We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…