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Related papers: Perfect hedging in rough Heston models

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Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst…

Statistics Theory · Mathematics 2024-02-16 Carsten Chong , Marc Hoffmann , Yanghui Liu , Mathieu Rosenbaum , Grégoire Szymanski

Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance…

Portfolio Management · Quantitative Finance 2008-12-10 N. Lazrieva , T. Toronjadze

We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…

Portfolio Management · Quantitative Finance 2019-05-17 Nicole Bäuerle , Sascha Desmettre

Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…

Computational Finance · Quantitative Finance 2025-03-07 Yiheng Ding , Gangnan Yuan , Dewei Zuo , Ting Gao

We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the…

Mathematical Finance · Quantitative Finance 2021-05-04 Christian Bayer , Fabian Andsem Harang , Paolo Pigato

We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…

Mathematical Finance · Quantitative Finance 2020-07-09 John Armstrong , Claudio Bellani , Damiano Brigo , Thomas Cass

In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error…

Probability · Mathematics 2017-09-19 Paolo Di Tella , Martin Haubold , Martin Keller-Ressel

We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…

Probability · Mathematics 2019-05-15 Ben Hambly , Nikolaos Kolliopoulos

In Gatheral et al. 2018, first posted in 2014, volatility is characterized by fractional behavior with a Hurst exponent $H < 0.5$, challenging traditional views of volatility dynamics. Gatheral et al. demonstrated this using realized…

Statistical Finance · Quantitative Finance 2024-09-06 Saad Mouti

We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models…

Pricing of Securities · Quantitative Finance 2015-03-20 Alvise De Col , Alessandro Gnoatto , Martino Grasselli

It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This…

Statistical Finance · Quantitative Finance 2017-02-10 Giulia Livieri , Saad Mouti , Andrea Pallavicini , Mathieu Rosenbaum

A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…

Pricing of Securities · Quantitative Finance 2017-10-23 Christian Bayer , Peter K. Friz , Paul Gassiat , Joerg Martin , Benjamin Stemper

How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as…

Computational Finance · Quantitative Finance 2019-11-25 Eduardo Abi Jaber

In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…

Pricing of Securities · Quantitative Finance 2019-10-21 Arunangshu Biswas , Anindya Goswami , Ludger Overbeck

We train an LSTM network based on a pooled dataset made of hundreds of liquid stocks aiming to forecast the next daily realized volatility for all stocks. Showing the consistent outperformance of this universal LSTM relative to other…

Statistical Finance · Quantitative Finance 2022-06-29 Mathieu Rosenbaum , Jianfei Zhang

We study two complementary methodologies for calibrating implied volatility surfaces: analytical approximations and data-driven models based on rough path theory. On the analytical side, we revisit a second-order asymptotic expansion for…

Mathematical Finance · Quantitative Finance 2026-05-11 Elisa Alòs , Òscar Burés , Rafael de Santiago , Josep Vives

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

Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that…

Risk Management · Quantitative Finance 2026-04-03 Adele Ravagnani , Mattia Chiappari , Andrea Flori , Piero Mazzarisi , Marco Patacca

We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in…

Trading and Market Microstructure · Quantitative Finance 2016-09-19 El Euch Omar , Fukasawa Masaaki , Rosenbaum Mathieu

In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…

Statistics Theory · Mathematics 2024-06-17 Carsten Chong , Marc Hoffmann , Yanghui Liu , Mathieu Rosenbaum , Grégoire Szymanski