Related papers: Risk measures with non-Gaussian fluctuations
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the…
Value-at-risk is one of the important subjects that extensively used by researchers and practitioners for measuring and managing uncertainty in financial markets. Although value-at-risk is a common risk control instrument, but there are…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution…
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the…
There are various metrics for financial risk, such as value at risk (VaR), expected shortfall, expected/unexpected loss, etc. When estimating these metrics, it was very common to assume Gaussian distribution for the asset returns, which may…
The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are…
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…
We present a computational method for measuring financial risk by estimating the Value at Risk and Expected Shortfall from financial series. We have made two assumptions: First, that the predictive distributions of the values of an asset…
Option pricing formulas are derived from a non-Gaussian model of stock returns. Fluctuations are assumed to evolve according to a nonlinear Fokker-Planck equation which maximizes the Tsallis nonextensive entropy of index $q$. A generalized…
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions…
Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For…
We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational…
We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric…
Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management…
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…
We present a model of financial markets originally proposed for a turbulent flow, as a dynamic basis of its intermittent behavior. Time evolution of the price change is assumed to be described by Brownian motion in a power-law potential,…
This paper aims to more effectively manage and mitigate stock market risks by accurately characterizing financial market returns and volatility. We enhance the Stochastic Volatility (SV) model by incorporating fat-tailed distributions and…
The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…