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We consider the exponential functional $A_{\infty}=\int_0^{\infty} e^{\xi_s} ds$ associated to a Levy process $(\xi_t)_{t \geq 0}$. We find the asymptotic behavior of the tail of this random variable, under some assumptions on the process…

Probability · Mathematics 2007-05-23 Mejane Olivier

The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities decay as exp(-lambda|x|) or…

Statistical Mechanics · Physics 2008-12-02 Sergei Levendorskii

We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the…

Mathematical Finance · Quantitative Finance 2017-02-08 Archil Gulisashvili , Frederi Viens , Xin Zhang

Inspired by recent lattice measurements, we determine the short-distance (a << r << 1/pi T) as well as large-frequency (1/a >> omega >> pi T) asymptotics of scalar (trace anomaly) and pseudoscalar (topological charge density) correlators at…

High Energy Physics - Phenomenology · Physics 2010-12-09 M. Laine , M. Vepsalainen , A. Vuorinen

We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first centered absolute moment of $S$. We show that…

Pricing of Securities · Quantitative Finance 2019-07-10 Johannes Muhle-Karbe , Marcel Nutz

In the present paper, a decomposition formula for the call price due to Al\`{o}s is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the…

Computational Finance · Quantitative Finance 2019-05-16 Archil Gulisashvili , Raúl Merino , Marc Lagunas , Josep Vives

By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…

Classical Analysis and ODEs · Mathematics 2015-11-25 Karen Ogilvie , Adri B. Olde Daalhuis

We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…

Statistical Finance · Quantitative Finance 2025-02-12 Carsten H. Chong , Viktor Todorov

We study how delegating pricing to large language models (LLMs) can facilitate collusion in a duopoly when both sellers rely on the same pre-trained model. The LLM is characterized by (i) a propensity parameter capturing its internal bias…

Theoretical Economics · Economics 2026-03-24 Shengyu Cao , Ming Hu

This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…

Mathematical Finance · Quantitative Finance 2024-05-17 Alexander Gairat , Vadim Shcherbakov

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…

Probability · Mathematics 2022-03-01 Robert Stelzer , Bennet Ströh

Discretization effects of lattice QCD are described by Symanzik's effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $\sim a^n [\bar g^2(a^{-1})]^{\hat\gamma_1} \sim…

High Energy Physics - Lattice · Physics 2020-03-18 Nikolai Husung , Peter Marquard , Rainer Sommer

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly…

Probability · Mathematics 2019-05-13 Gane Samb Lo , Mohammad ahsanullah

We develop novel estimation procedures with supporting econometric theory for a dynamic latent-factor model with high-dimensional asset characteristics, that is, the number of characteristics is on the order of the sample size. Utilizing…

Econometrics · Economics 2024-05-27 Adam Baybutt

In this paper we use Malliavin Calculus techniques in order to obtain expressions for the short-time behavior of the at-the-money implied volatility (ATM-IV) level and skew for a jump-diffusion stock price. The diffusion part is assumed to…

Mathematical Finance · Quantitative Finance 2025-03-31 Elisa Alòs , Òscar Burés , Josep Vives

In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while…

Probability · Mathematics 2016-03-25 Andreas Basse-O'Connor , Raphaël Lachièze-Rey , Mark Podolskij

In this paper similar to [P. Carr, A. Itkin, 2019] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both…

Computational Finance · Quantitative Finance 2023-09-27 Andrey Itkin

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for…

Computational Finance · Quantitative Finance 2019-03-25 Omar El Euch , Masaaki Fukasawa , Jim Gatheral , Mathieu Rosenbaum

We consider a finite dimensional deterministic dynamical system with a global attractor A with a unique ergodic measure P concentrated on it, which is uniformly parametrized by the mean of the trajectories in a bounded set D containing A.…

Probability · Mathematics 2013-03-21 Michael Högele , Ilya Pavlyukevich

We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…

Probability · Mathematics 2007-05-23 Jean Jacod