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We examine the small expiry behaviour of European call options in stock price models of exponential L\'evy type. In most cases of interest, we are able to identify the exact small expiry asymptotics. In "complete generality" we are able to…

Pricing of Securities · Quantitative Finance 2008-12-02 Michael Roper

Motivated by marginals-mimicking results for It\^o processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target…

Pricing of Securities · Quantitative Finance 2016-06-15 Stefano De Marco , Peter Friz

We investigate the asymptotics of eigenvalues of sample covariance matrices associated with a class of non-independent Gaussian processes (separable and temporally stationary) under the Kolmogorov asymptotic regime. The limiting spectral…

Probability · Mathematics 2019-10-11 Tiebin Mi , Robert Caiming Qiu

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

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…

Pricing of Securities · Quantitative Finance 2016-08-08 Sidi Mohamed Aly

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems…

Statistics Theory · Mathematics 2010-02-26 Yazhen Wang , Jian Zou

This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…

Probability · Mathematics 2024-10-04 Michael Levine , Xiaoguang Wang , Jian Frank Zou

Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface…

Mathematical Finance · Quantitative Finance 2022-11-16 Florian Bourgey , Stefano De Marco , Peter K. Friz , Paolo Pigato

We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and…

Pricing of Securities · Quantitative Finance 2019-08-19 Dan Pirjol , Jing Wang , Lingjiong Zhu

We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…

Probability · Mathematics 2018-12-21 B. Horvath , A. Jacquier , C. Lacombe

This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a H\"older continuous payoff function in a local…

Mathematical Finance · Quantitative Finance 2024-04-30 Jaehyun Kim , Hyungbin Park , Jonghwa Park

We derive the short-maturity asymptotics for Asian option prices in local-stochastic volatility (LSV) models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the…

Pricing of Securities · Quantitative Finance 2025-09-24 Dan Pirjol , Lingjiong Zhu

We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The…

Pricing of Securities · Quantitative Finance 2026-01-27 Desen Guo , Dan Pirjol , Xiaoyu Wang , Lingjiong Zhu

We study the asymptotic behaviour of sequences of multivariate random variables representing the number of occurrences of a given set of symbols in a word of length $n$ generated at random according to a rational stochastic model. Assuming…

Probability · Mathematics 2026-02-03 Massimiliano Goldwurm , Claudio Macci , Marco Vignati , Elena Villa

Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…

Statistics Theory · Mathematics 2025-07-09 Mitsuki Kobayashi , Yuto Nishiwaki , Yasutaka Shimizu , Nobutoki Takaoka

We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options…

Pricing of Securities · Quantitative Finance 2024-05-08 Dan Pirjol , Lingjiong Zhu

In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders.…

Probability · Mathematics 2018-09-19 Sergio ALbeverio , Francesco Cordoni , Luca Di Persio , Gregorio Pellegrini

In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dG^{H}_{s}$, where $u$ is a $\beta$-H\"older continuous process with $\beta >1-H$ and $G^H$ is a self-similar Gaussian…

Probability · Mathematics 2019-09-17 Salwa Bajja , Qian Yu

Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated, in particular when X 1 is not…

Probability · Mathematics 2021-01-21 Fabien Brosset , Thierry Klein , Agnès Lagnoux , Pierre Petit

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the…

Pricing of Securities · Quantitative Finance 2009-06-03 A. Gulisashvili