Unified approach to risk measurement using Skew Exponential Power distribution.
problem Direct measurement of market risk with improved asymmetry and non-linearity.
method Unified Bayesian Conditional Autoregressive Risk Measures using Skew Exponential Power distribution with semiparametric P-spline approximation.
result Demonstrated effectiveness on real data of five stock market indices.
A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.
problem Efficient computation of derivatives for skew-symmetric matrices.
method Characterization of invertibility, construction of nearby logarithm, and efficient implementation.
result Explicit formulae for differentiation and its inverse of skew-symmetric matrix exponentials.
Extends Stein's lemma to exponential-family mixtures for gradient computation.
problem Computing gradients for complex distributions with weak assumptions.
method Generalizes Stein's lemma to exponential-family mixtures and applies it to reparameterization trick.
result Derives new gradient identities for various distributions.
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are …
Volatility models must be rough to match market skew.
problem Inconsistent non-rough volatility models with power law volatility skew.
method Asymptotic expansion and continuous price dynamics analysis.
result Volatility must be rough to align with market skew.
Characterizes the local diffeomorphism structure of the exponential in the set of skew-symmetric matrices.
problem Characterizing the local diffeomorphism structure of the exponential in the set of skew-symmetric matrices.
method Introduce the diffeomorphic logarithm of special orthogonal matrices and an efficient algorithm.
result The region containing the principal logarithm has a special multiplicity structure.
Skewness dispersion predicts future stock market returns, especially in months with monetary policy announcements.
problem Predicting future stock market returns using skewness dispersion.
method Cross-sectional analysis of firm-level realized skewness and stock market returns.
result Skewness dispersion is a significant predictor of future stock market returns, robust to various estimation methods.
Paper proves SVV model reproduces power-law skew in implied volatilities.
problem Reproducing power-law behavior in implied volatility skew.
method Analytical proof using Malliavin calculus and Volterra kernel selection.
result SVV model reproduces power-law skew under correct kernel choice.
We investigate the connections between the differential-geometric properties of the exponential map from the space of real skew symmetric matrices onto the group of real special orthogonal matrices and the manifold of real orthogonal matrices equipped with the Riemannian structure induced by the Frobenius metric.
The paper classifies surfaces with constant skew curvature in 3-space forms.
problem Classifying surfaces with constant skew curvature in 3-space forms.
method Variational characterization and flow of binormal vector field.
result Classification of rotational surfaces with constant skew curvature.
A new family of conformal test martingales based on Legendre polynomials for online exchangeability testing.
problem Detecting variance, skewness, and higher-order deviations from uniformity in online data.
method A family of conformal test martingales based on shifted Legendre polynomials.
result The Variational Legendre Jumper reduces exponential scaling to linear time with minimal loss in power.
New condition ensures submanifolds are skew in small areas.
problem Ensuring submanifolds are skew in Euclidean space.
method Introduces a third-order differential condition.
result Constructs improved totally skew embeddings for Rn. Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution.…
Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we cond…
We develop a new method to price SOFR futures contracts considering convexity, skew, and smile.
problem Analyzing and pricing SOFR futures contracts with convexity, skew, and smile adjustments.
method A perturbative formalism based on a time-ordered exponential series to solve the backward-Kolmogorov diffusion PDE.
result An analytic pricing formula for SOFR futures contracts that incorporates convexity, skew, and smile adjustments.
Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
The paper examines the short-time implied volatility of additive processes and finds key parameters.
problem Characterizing the short-time implied volatility of equity markets.
method Examined pure jump exponential additive processes with power-law scaling parameters.
result The implied volatility is consistent with equity market characteristics if and only if β=1 and δ=-1/2.
Study curvature properties of specific Riemannian manifolds with skew-circulant structures.
problem Investigate curvature of Riemannian manifolds with a particular tensor structure.
method Analyze 4D Riemannian manifolds with right skew-circulant tensor S, invariant under S and g, focusing on Ricci tensor and sectional curvatures.
result Obtained properties of curvature tensors and sectional curvatures for specific manifolds.
This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and ku…
Counterexample found to estimate for skew-symmetric tensors.
problem Estimate for skew-symmetric tensors was claimed and used for classification results.
method Analysis of the estimate in arXiv:2103.15482.
result Counterexample disproves the estimate for skew-symmetric tensors.
We derive measure change formulae required to price midcurve swaptions in the forward swap annuity measure with stochastic annuities' ratios. We construct the corresponding linear and exponential terminal swap rate pricing models and show how they capture the midcurve swaption correlation skew.
A new distribution family extends the α-stable distribution with a degree of freedom parameter.
problem Lack of moments in the α-stable distribution. method Wright function framework to combine and extend distribution families.
result Generalized α-stable distribution with valid moments. Paper derives new option pricing formulas and approximations for a local volatility model with discontinuity.
problem Modeling extreme ATM skew in a local volatility model with discontinuity.
method Uses joint distribution of Skew Brownian motion and its functionals to derive option pricing formulas and approximations.
result Derives an approximation of option prices by Black-Scholes prices, simplifying skew behavior.
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
Study of spheres and circles on a manifold with a specific metric structure.
problem Understanding geometric objects on a manifold with a skew-circulant structure.
method Analyzing hyper-spheres, spheres, and circles in a tangent space of a 4D manifold with a skew-circulant tensor structure.
result Characterization of geometric objects under an indefinite metric.
Model predicts jump risk premia influencing cryptocurrency futures and option performance.
problem Capturing asymmetric and time-varying skewness in cryptocurrency returns.
method Bivariate Hawkes process with positive and negative jump premia.
result Inferred jump risk premia predict futures cost of carry and option performance.
New model captures time-varying volatility with stochastic exponential tails.
problem Capturing time-varying volatility and stochastic skewness in financial markets.
method Normal Tempered Stable distribution with time-varying parameter.
result Model better explains market option prices with stochastic exponential tails.
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot…
We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these featu…
Study local volatility from rough volatility models, finding new skew rule.
problem Understanding local volatility from rough volatility models.
method Analyzing asymptotic behavior of local volatility surface generated by rough stochastic volatility models.
result New skew rule: ratio of implied and local vol skews tends to 1/(H + 3/2).
A pseudo-Riemannian manifold is said to be spacelike Jordan IP if the Jordan normal form of the skew-symmetric curvature operator depends upon the point of the manifold, but not upon the particular spacelike 2-plane in the tangent bundle at that point. We use methods of algebraic topology to classify connected spacelik…
A new Riemannian manifold with skew-circulant structures and its associated locally conformal Kähler manifold are studied.
problem Exploring new Riemannian manifolds with specific tensor structures.
method Defined a tensor on a 4D Riemannian manifold with skew-circulant properties, constructed a Lie group, and studied associated Hermitian manifolds.
result The associated Hermitian manifold is a locally conformal Kähler manifold.
Anomalous diffusions explain market behavior of implied volatility better than standard models.
problem Reconciling market behavior with standard financial models.
method Analyzed continuous-time random walks with power-law distributed innovation times.
result Anomalous diffusions provide a more consistent fit for implied volatility.
The paper examines short-term volatilities in equity indexes using a ranking procedure.
problem Understanding short-term behaviors of implied volatility in equity markets.
method Using a ranking procedure to model equity index dynamics, the paper investigates the short-term volatilities of derivatives written on indexes.
result The models reconcile the long memory of volatilities and power law of ATM skews in equity markets.
We derive an extremal fractional Gaussian by employing the Lévy-Khintchine theorem and Lévian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and exponentially convergent option-pricing formula for fractional markets. We also carry o…
New rough stochastic volatility models using log-modulated fractional Brownian motion.
problem Analyzing rough stochastic volatility models over the range 0≤H<1/2. method Introducing log-modulated fractional Brownian motion (log-fBm) to handle H=0 and analyze over the full range. result Obtained skew asymptotics of log(1/T)−pTH−1/2 as To0 for H≥0, no flattening of skew as Ho0. We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal…
Layer normalization improves federated learning with skewed labels.
problem Label skewness in federated learning datasets.
method Identified feature normalization as key mechanism; applied to latent features before classifier.
result Normalization accelerates global training and improves convergence under extreme label shift.
New structure for quantum algebra representations.
problem Understanding representations of quantum algebras.
method Constructing a quotient category of annular quantum gln webs. result Equivalent to finite dimensional representations of quantum Levi subalgebras.
Study improves statistical power for detecting algorithmic bias in educational data.
problem Challenges in measuring algorithmic bias using ABROCA due to skewed distribution.
method Investigates ABROCA's distributional properties and proposes nonparametric randomization tests.
result ABROCA-based bias assessments are underpowered in typical EDM sample sizes.
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…
Study compares exponential and power-law kernels in modeling high-frequency trading data.
problem Modeling high-frequency trading data with specific kernel types.
method Proposes and analyzes two bivariate Hawkes processes with exponential and power-law kernels.
result Identifies strengths and limitations of exponential and power-law kernels for high-frequency trading data.
Ormerod and Mounfield analysed GDP data of 17 leading capitalist economies from 1870 to 1994 and concluded that the frequency of the duration of recessions is consistent with a power-law. But in fact the data is consistent with an exponential (Boltzmann-Gibbs) law.
The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection o…
This study shows that certain cohomology groups of symplectic manifolds are always even-dimensional.
problem Understanding the cohomology structure of symplectic manifolds.
method Constructing and deforming a skew-adjoint operator to prove the vanishing property.
result The even dimensionality of even-degree cohomology groups in (4n+2)-dimensional symplectic manifolds.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.