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Related papers: Local volatility under rough volatility

200 papers

Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and…

Statistical Finance · Quantitative Finance 2014-03-21 Zeyu Zheng , Zhi Qiao , Joel N. Tenenbaum , H. Eugene Stanley , Baowen Li

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried…

Mathematical Finance · Quantitative Finance 2019-10-31 Mehdi Tomas , Mathieu Rosenbaum

The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the…

Mathematical Finance · Quantitative Finance 2022-08-01 Fabien Le Floc'h

In financial terms, an implied volatility surface can be described by its term structure, its skewness and its overall volatility level. We use a PCA variational auto-encoder model to perfectly represent these descriptors into a latent…

Pricing of Securities · Quantitative Finance 2023-06-09 Zheng Gong , Wojciech Frys , Renzo Tiranti , Carmine Ventre , John O'Hara , Yingbo Bai

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 provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston…

Computational Finance · Quantitative Finance 2023-10-09 Christian Bayer , Simon Breneis

Following-up Fukasawa and Gatheral (Frontiers of Mathematical Finance, 2022), we prove that the BBF formula, the SABR formula, and the rough SABR formula provide asymptotically arbitrage-free approximations of the implied volatility under,…

Mathematical Finance · Quantitative Finance 2022-01-19 Masaaki Fukasawa

We introduce a novel rough Bergomi (rBergomi) model featuring a variance-driven exponentially weighted moving average (EWMA) time-dependent Hurst parameter $H_t$, fundamentally distinct from recent machine learning and wavelet-based…

Mathematical Finance · Quantitative Finance 2025-09-09 Jayanth Athipatla

In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…

Mathematical Finance · Quantitative Finance 2020-08-05 Christian Bayer , Jinniao Qiu , Yao Yao

We propose a two-step framework for predicting the implied volatility surface over time without static arbitrage. In the first step, we select features to represent the surface and predict them over time. In the second step, we use the…

Statistical Finance · Quantitative Finance 2022-01-04 Wenyong Zhang , Lingfei Li , Gongqiu Zhang

We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…

Pricing of Securities · Quantitative Finance 2012-07-17 Aleksandar Mijatović , Peter Tankov

Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…

Applications · Statistics 2022-05-18 Kai Yin , Anirban Mondal

We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an It\^o semimartingale with jumps and general…

Statistics Theory · Mathematics 2024-11-20 Markus Bibinger

This paper advances interest rate modeling in the post-LIBOR era by introducing rough stochastic volatility into the Forward Market Model (FMM). We establish a rigorous asymptotic expansion of swaption implied volatility, connecting the FMM…

Mathematical Finance · Quantitative Finance 2025-10-01 Reo Adachi , Masaaki Fukasawa , Naoki Iida , Mitsumasa Ikeda , Yo Nakatsu , Ryota Tsurumi , Tomohisa Yamakami

We present a Hawkes modeling of the volatility surface's high-frequency dynamics and show how the Hawkes kernel coefficients govern the surface's skew and convexity. We provide simple sufficient conditions on the coefficients to ensure…

Trading and Market Microstructure · Quantitative Finance 2020-12-22 Bastien Baldacci

Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…

Mathematical Finance · Quantitative Finance 2026-05-19 Wolfgang Schadner

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to…

Numerical Analysis · Mathematics 2014-08-27 Vinicius V. L. Albani , Jorge P. Zubelli

This paper presents a novel approach to stochastic volatility (SV) modeling by utilizing nonparametric techniques that enhance our ability to capture the volatility of financial time series data, with a particular emphasis on the…

Computation · Statistics 2025-02-18 Yudong Feng , Ashis Gangopadhyay

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to…

Statistical Finance · Quantitative Finance 2008-12-02 Yingying Li , Per A. Mykland

The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied…

Computational Finance · Quantitative Finance 2020-07-13 Christian Bayer , Chiheb Ben Hammouda , Raul Tempone