arXiv research

Paper proposes a new Taylor moment expansion for non-linear Gaussian filtering and smoothing.

Paper provides Edgeworth expansions for network moments, improving accuracy of sampling distributions.

Approximates discounted moments for financial products using polynomial expansions.

The paper generalizes the moment map interpretation of scalar curvature in Kähler geometry.

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s_+$ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: $σ_{BS}( k,T)^{2}T\sim Ψ(s_+-1) \times k$ (Roger Lee's moment…

The paper provides a series expansion for Asian option pricing using orthogonal polynomials.

Study local expansions of continuous-time processes using Ito signature properties.

Derives a series expansion for Asian option pricing with polynomial jump-diffusion moments.

The paper generalizes a moment map interpretation of scalar curvature in Kähler geometry.

Corrected proof for C^2UCB contextual combinatorial bandit's regret bound.

In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function) by matching moments of increasing order. Because, as shown in literature, the pri…

A method to estimate functions of the return using its moments in reinforcement learning.

Develops a new mathematical framework for financial asset pricing.

We consider a stochastic volatility model where the moment generating function of the logarithmic price is finite only on part of the real line. Using a new Tauberian result obtained in [1] and [2], we show that the knowledge of the moment generating function near its critical moment gives a sharp asymptotic expansion …

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our numerical results show that a second order expansion provides accurate prices o…

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the same superposition of Black…

Theoretical models applied to option pricing should take into account the empirical characteristics of the underlying financial time series. In this paper, we show how to price basket options when assets follow a shifted log-normal process with jumps capable of accommodating negative skewness. Our technique is based on…

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (200…

The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …

The article introduces inferential moments for analyzing uncertain multivariable systems.

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correcti…

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple eq…

This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Using a multivariate normal Copula function for the joint default probabilities we show that retaining the first few moments of the portfolio default l…

A new method approximates option pricing in stochastic interest rate markets.

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including probabilistic topic models and latent linear Bayesian networks, using only secon…

A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.

Corrected moment-based methods improve inference in topic model regression.

This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Under fairly general assumptions for the distribution of the total net assets of a set of firms we show that retaining the first few moments of the por…

The paper provides rigorous guarantees for m-out-of-n bootstrap estimators of sample quantiles.

Develops state-space deep Gaussian processes for irregular signals.

Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator acting on smooth functions on (O,g) determines the moment polytope of O, and hence by Delzant's theorem det…

This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…

Roy's `Safety First' criterion for selecting one risky asset from many is adapted to the case of non-normal returns, via Cornish Fisher expansion. The resulting investment objective is consistent with first order stochastic dominance, and is equal to the Sharpe ratio for the case of normal returns. An investor selectin…

TACE unifies scalar and tensorial modeling in Cartesian space for accurate, stable, and efficient atomistic predictions.

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digit…

EigenVI uses orthogonal function expansions for efficient variational inference.

Maximal concentration bounds for stochastic approximation with heavy-tailed noise.

Study improves BN TTA under distribution shift using higher-order asymptotics.

CO2 algorithm creates coresets for generic smooth divergences efficiently.

Formula calculates Riemann-Roch number for singular symplectic quotients.

This work examines the sensitivity of energy distance to mean differences compared to covariance differences.

Researchers develop explicit approximations for European put options in stochastic volatility models.

Study spectral density of neural networks using resolvent method.

The paper examines how the angle between inputs in ReLU networks decreases with depth, impacting training.

Study on kernel tests for high-dimensional data, focusing on MMD and CLT.