Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale…
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48 results for “lognormal dynamics”
Alternative method preserves positivity in interest rate interpolation.
problem Positivity issue in interest rate interpolation.
method Alternative method preserving Markovian properties and positivity.
result Guaranteed positivity of all interpolated rates.
Modified lognormal distribution with flexible tails for skewed data.
problem Skewed and fat-tailed data in natural and engineering datasets.
method Developed a family of three-parameter non-Gaussian probability density functions based on generalized kappa-exponential and kappa-logarithm functions.
result Closed-form analytic expressions for statistical functions and maximum-likelihood estimation.
We consider a simple stochastic model of a urban rental housing market, in which the interaction of tenants and landlords induces rent fluctuations. We simulate the model numerically and measure the equilibrium rent distribution, which is found to be close to a lognormal law. We also study the influence of the density …
Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.
problem Approximating sums of lognormal random variables accurately.
method Introduces new approximations based on weighted distribution theory, emphasizing comonotonicity and moment matching.
result Approximations perform better than classical methods, especially in the right tail of the distribution.
The paper presents an approximate formula for European mortgage options pricing.
problem Pricing European mortgage options with accuracy and efficiency.
method Approximation of the underlying price distribution using lognormal distributions and matching moments.
result The proposed formula provides a good approximation with high accuracy compared to Monte Carlo simulations.
Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. …
This paper bridges Kahler geometry and quantum mechanics in lognormal statistical models.
problem Evolution of spectral curves in Siegel Jacobi space through Schrodinger equation.
method Kahler geometry induced on lognormal statistical manifold, Dombrowski's construction.
result Time-dependent Schrodinger equation with varying energy.
Lower bound found for volatility swap in SABR model.
problem Finding a lower bound for volatility swap in SABR model.
method Short time to maturity limit analysis of conditionally lognormal SABR model.
result Zero vanna implied volatility is a lower bound for volatility swap strike.
Analyzes premium data of Indian non-life insurers, finding GEV distribution best fits Lognormal and GEV extremes.
problem Modeling premiums of non-life insurance companies in India.
method Empirical analysis using Lognormal, GEV, and GPD distributions.
result Generalized Extreme Value distribution best fits premium data for ten Indian non-life insurers.
On absence of steady state in the Bouchaud-Mézard network modelcond-mat.stat-mech
For finite networks, Bouchaud-Mézard model's steady state is lognormal and quasi-stationary.
problem Finite network effects on steady state distribution in Bouchaud-Mézard model.
method Analysis of Bouchaud-Mézard model with finite number of nodes.
result Time-dependent lognormal mean and quasi-stationary inverse gamma distribution.
The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between…
A dynamic model of the social relations between workers and capitalists is introduced. The model is deduced from the assumption that the law of value is an organising principle of modern economies. The model self-organises into a dynamic equilibrium with statistical properties that are in close qualitative and in many …
In this paper we introduce a simple model for a financial market characterized by a single stock or good and an interplay between two different traders populations, chartists and fundamentalists, which determine the price dynamic of the stock. The model has been inspired by the microscopic Lux-Marchesi model (T.Lux, M.…
We present a simple hybrid dynamical model as a tool to investigate behavioral strategies based on trend following. The multiplicative symbolic dynamics are generated using a lognormal diffusion model for the at-the-money implied volatility term structure. Thus, are model exploits information from derivative markets to…
In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE) admitting a unique strong solution and whose density evolves as a mixture of Gaussian d…
Paper develops a new method for calculating the probability density of a fractional SABR model.
problem Lack of probability density calculations for lognormal fractional SABR model.
method Bridge representation in Fourier space, small time asymptotic expansion, large deviations principle derivation.
result Developed a method to calculate the probability density of fractional SABR model.
We prove lognormal distribution for symmetric perceptron model, solving key conjectures.
problem Understanding the performance of learning algorithms in neural networks.
method Lognormal distribution characterization and small graph conditioning method.
result Established lognormal distribution and several conjectures for the symmetric perceptron model.
The Limits of Lognormal: Assessing Cryptocurrency Volatility and VaR using Geometric Brownian Motionq-fin.RM
Study benchmarks cryptocurrency risk using GBM, revealing Lognormal limitations.
problem Tackles limitations of Lognormal assumption in modeling cryptocurrency volatility and VaR.
method Applies Geometric Brownian Motion (GBM) with Maximum Likelihood Estimation and correlated Monte Carlo Simulation.
result Observed limitations of Lognormal assumption in cryptocurrency volatility and VaR calculations.
Cross-Ownership as a Structural Explanation for Over- and Underestimation of Default Probabilityq-fin.RM
Based on the work of Suzuki (2002), we consider a generalization of Merton's asset valuation approach (Merton, 1974) in which two firms are linked by cross-ownership of equity and liabilities. Suzuki's results then provide no arbitrage prices of firm values, which are derivatives of exogenous asset values. In contrast …
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in te…
Study examines pricing of target volatility options in fractional SABR model.
problem Pricing target volatility options in the lognormal fractional SABR model.
method Used Ito's calculus for a theoretical replicating strategy and derived approximations and closed-form expressions.
result Accuracy of approximations for target volatility option pricing in various parameter ranges.
We derive variance-optimal hedging strategies for SABR and rough Bergomi models.
problem Finding efficient hedging strategies in lognormal SABR and rough Bergomi models.
method Analytic expressions for variance-optimal hedging strategies and mean-square hedging errors.
result The variance-optimal hedging strategy in SABR coincides with Delta adjustment.
We empirically investigate distributions of individual consumption expenditure f or four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. W e use graphical techniques to test for normality and lognormality of these dis…
Optimal fund deployment strategy under uncertain deal arrivals.
problem Deciding when to invest in deals with uncertain future arrivals.
method Formulated as CTMDP, solved via ADP with QMC sampling.
result Developed interpretable acceptance policy outperforming baseline.
The paper approximates rough lognormal model using Markovian processes.
problem Modeling rough lognormal volatility in financial markets.
method Applying Markovian approximation to fractional Brownian motion (DO process) to lognormal volatility model.
result Uniformly good approximation of fractional BM for all Hurst exponents H ∈ [0,1].
Paper improves stochastic collocation for local volatility models.
problem Improving local volatility models for assets with boundaries.
method Applied stochastic collocation to lognormal distributions, derived analytical local volatility.
result Simple analytical Dupire local volatility derived from option prices.
First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time-value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the lognormal implied volatil…
Volatility in Financial Markets: Stochastic Models and Empirical Resultscond-mat.stat-mech
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pd…
The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problemq-fin.PR
This paper uses basket option formulas to price vanilla options with discrete dividends.
problem Pricing vanilla options on stocks with discrete cash dividends.
method Uses existing basket option formulas for European options on a single asset with cash dividends in the piecewise lognormal model.
result Explains the use of basket option formulas for a specific problem in the piecewise lognormal model.
New method uses SBI to infer magnetorotational properties of isolated pulsars.
problem Constrain magnetorotational properties of isolated Galactic radio pulsars.
method Combines population synthesis with SBI to model neutron star birth and evolution.
result Inferred , for lognormal distributions.
Paper presents new expansions for option pricing with cash dividends.
problem No exact formula for European options with cash dividends.
method Uses Etore and Gobet's technique for piecewise lognormal process with jumps.
result Provides more robust first, second, and third-order expansions.
Modified Vanna-Volga method constructs Normal volatility smiles.
problem No method existed for constructing Normal volatility smiles.
method Modified Vanna-Volga method applied to Normal volatilities.
result The Vanna-Volga method can easily fit both convex and concave smiles.
A New Approach to Personal Income Distributioncond-mat.stat-mech
The results of R^2 dynamical random surface model (2-dimensional quantum gravity with a term) are applied to explain the personal income distribution. A scale invariance exists if there is not the term in the action. The R^2 term provides a typical scale and breaks the scale invariance explicitly in the low…
The widening inequality in income distribution in recent years, and the associated excessive pay packages of CEOs in the U.S. and elsewhere, is of growing concern among policy makers as well as the common person. However, there seems to be no satisfactory answer, in conventional economic theories and models, to the fun…
Fenton-Wilkinson Order Statistics and German Tanks: A Case Study of an Orienteering Relay Racestat.ML
Lognormal distribution used for predicting team rankings in an orienteering relay race.
problem Predicting final team rankings in an orienteering relay race.
method Used lognormal distribution and Fenton-Wilkinson approximations for order statistics.
result Accurate predictions of team rankings using order statistics.
Addressing the Impact of Data Truncation and Parameter Uncertainty on Operational Risk Estimatesq-fin.RM
Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the P…
The author seeks to develop a model to alter the bid-offer spread, currently quoted by market makers, that varies with the market and trading conditions. The dynamic nature of financial markets and trading, as with the rest of social sciences, where changes can be observed and decisions can be made by participants to i…
Modeling volatility with Chained Gamma Distributions for financial time series.
problem Volatility clustering in financial time series, especially in estimating temporal autocorrelation of logarithmic variance of returns.
method Dynamic Bayesian Network with conjugate prior relation of normal-gamma and gamma-gamma, using variational methods for quick approximate solutions.
result The model can express heavier tails than Gaussians, achieving positive excess kurtosis, and runs faster than Monte Carlo methods.
Pareto's Law of Income Distribution: Evidence for Germany, the United Kingdom, and the United Statesphysics.soc-ph
We analyze three sets of income data: the US Panel Study of Income Dynamics PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic Panel (GSOEP). It is shown that the empirical income distribution is consistent with a two-parameter lognormal function for the low-middle income group (97%-99% of …
The study quantifies Brexit risk using SABR dynamics and Bayesian methods.
problem Measuring tail risk in EUR-GBP options related to Brexit.
method Data-driven statistical indicator, lognormal SABR dynamics, Bayesian estimation, inverse calibration problem, Markov chain Monte Carlo.
result A closed-form expression for the martingale defect quantifying tail risk.
This paper uses entropy to derive stock price dynamics and option valuation.
problem Deriving stock price dynamics and option valuation from information constraints.
method Develops an entropic inference framework to derive stochastic processes from information constraints, representing price changes through two channels: continuous and jump.
result The derived dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit.
This work presents an empirical study of the evolution of the consumer expenditure distribution in India during 1982-2007. We have used the National Sample Survey Organization data and analysed the expenditure distribution for the urban and rural sectors. It is found that this distribution is a mixture of two distribut…
Bayesian Deep Learning quantifies uncertainty in skewed climate data.
problem Uncertainty quantification for skewed, discrete-continuous data in climate modeling.
method Discrete-continuous Bayesian Deep Learning model with Gaussian and lognormal likelihoods.
result Lognormal distribution provides better uncertainty estimates at extremes.
New approach improves computational efficiency of Bass Local Volatility model.
problem Eliminate interpolation and improve computational efficiency in local volatility models.
method Combines local quadratic estimation and lognormal mixture tails for state price densities; uses trapezoidal rule for numerical convolutions.
result Proposed method outperforms traditional numerical methods in option pricing and market case studies.
In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tra…
This paper uses a kinetic approach to model financial agents and their impact on stock prices and wealth distribution.
problem Understanding power-laws in financial data and the causes behind them.
method A kinetic approach inspired by the Levy-Levy-Solomon model, incorporating model predictive control (MPC) for optimization.
result The stock price distribution exhibits power-law behavior for high-frequency traders and lognormal for long-term investors.
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of th…