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Related papers: Asymptotic arbitrage in the Heston model

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Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of…

Optimization and Control · Mathematics 2014-06-23 Martin Le Doux Mbele Bidima , Miklós Rásonyi

In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized…

Statistics Theory · Mathematics 2011-06-22 Markus Bibinger

Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…

Probability · Mathematics 2021-03-03 Sugata Ghosh , Asok K. Nanda

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…

Probability · Mathematics 2009-06-29 Bernard Bercu , Benoite de Saporta , Anne Gegout-Petit

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus…

Pricing of Securities · Quantitative Finance 2010-02-22 Jim Gatheral , Antoine Jacquier

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…

Probability · Mathematics 2016-09-21 Nathan E. Glatt-Holtz , Jonathan C. Mattingly , Geordie Richards

This article studies the finite sample behaviour of a number of estimators for the integrated power volatility process of a Brownian semistationary process in the non semi-martingale setting. We establish three consistent feasible…

Statistics Theory · Mathematics 2021-06-18 Phillip Murray , Riccardo Passeggeri , Almut E. D. Veraart , Mikko S. Pakkanen

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…

Statistics Theory · Mathematics 2016-09-15 Degui Li , Dag Tjøstheim , Jiti Gao

We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted…

Pricing of Securities · Quantitative Finance 2012-09-19 Mark H. A. Davis , Jan Obloj , Vimal Raval

In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…

Mathematical Finance · Quantitative Finance 2019-12-24 Gifty Malhotra , R. Srivastava , H. C. Taneja

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

In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…

Applications · Statistics 2016-12-13 Maryam Sohrabi , Mahmoud Zarepour

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

The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…

General Finance · Quantitative Finance 2011-03-08 Alexander Alvarez , Sebastian Ferrando , Pablo Olivares

In this paper we prove the asymptotic efficiency of the model selection procedure proposed by the authors in the first part. To this end we introduce the robust risk as the least upper bound of the quadratical risk over a broad class of…

Statistics Theory · Mathematics 2009-09-18 Victor Konev , Serguei Pergamenchtchikov

We apply the recent results of F. Hiai, M. Mosonyi and T. Ogawa [arXiv:0707.2020, to appear in J. Math. Phys.] to the asymptotic hypothesis testing problem of locally faithful shift-invariant quasi-free states on a CAR algebra. We use a…

Quantum Physics · Physics 2009-11-13 M. Mosonyi , F. Hiai , T. Ogawa , M. Fannes

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 study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull-White and Schobel-Zhu stochastic volatility models we give simple explicit expressions…

Pricing of Securities · Quantitative Finance 2013-10-03 Carole Bernard , Zhenyu Cui

Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $\sigma_t$. Here, we quantify how much information about $\sigma_t$ can be inferred from asset prices…

Statistical Finance · Quantitative Finance 2015-12-29 Nils Bertschinger , Oliver Pfante

We study, from the perspective of large financial markets, the asymptotic arbitrage opportunities in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was introduced by Sottinen and…

Probability · Mathematics 2018-04-05 Fernando Cordero , Lavinia Perez-Ostafe