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Related papers: Rough multifactor volatility for SPX and VIX optio…

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The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its…

Mathematical Finance · Quantitative Finance 2021-09-21 Qinwen Zhu , Grégoire Loeper , Wen Chen , Nicolas Langrené

Given the promising results on joint modeling of SPX/VIX smiles of the recently introduced quadratic rough Heston model, we consider a multi-asset market making problem on SPX and its derivatives, e.g. VIX futures, SPX and VIX options. The…

Mathematical Finance · Quantitative Finance 2022-12-21 Mathieu Rosenbaum , Jianfei Zhang

The rBergomi model under the physical measure consists of modeling the log-variance as a truncated Brownian semi-stationary process. Then, a deterministic change of measure is applied. The rBergomi model is able to reproduce observed market…

Pricing of Securities · Quantitative Finance 2023-11-06 Henrique Guerreiro , João Guerra

In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and…

Mathematical Finance · Quantitative Finance 2025-08-22 Giulia Di Nunno , Kęstutis Kubilius , Yuliya Mishura , Anton Yurchenko-Tytarenko

The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially…

Computational Finance · Quantitative Finance 2021-01-06 Ryan McCrickerd , Mikko S. Pakkanen

In this chapter we first briefly review the existing approaches to hedging in rough volatility models. Next, we present a simple but general result which shows that in a one-factor rough stochastic volatility model, any option may be…

Mathematical Finance · Quantitative Finance 2021-05-11 Masaaki Fukasawa , Blanka Horvath , Peter Tankov

Sparked by Al\`os, Le\'on, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the…

Pricing of Securities · Quantitative Finance 2018-10-09 Christian Bayer , Benjamin Stemper

We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is…

Computational Finance · Quantitative Finance 2022-07-19 Christian Bayer , Simon Breneis

We introduce the two-factor Quintic Ornstein-Uhlenbeck (OU) model, where volatility is modelled as a degree-five polynomial of the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian motion, each mean-reverting at a…

Mathematical Finance · Quantitative Finance 2026-04-23 Eduardo Abi Jaber , Shaun , Li

We consider the pricing of VIX options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate…

Computational Finance · Quantitative Finance 2025-01-28 Florian Bourgey , Stefano De Marco

We present a novel Monte Carlo based LSV calibration algorithm that applies to all stochastic volatility models, including the non-Markovian rough volatility family. Our framework overcomes the limitations of the particle method proposed by…

Mathematical Finance · Quantitative Finance 2019-10-01 Aitor Muguruza

Joint calibration to SPX and VIX market data is a delicate task that requires sophisticated modeling and incurs significant computational costs. The latter is especially true when pricing of volatility derivatives hinges on nested Monte…

Computational Finance · Quantitative Finance 2025-07-15 Fabio Baschetti , Giacomo Bormetti , Pietro Rossi

In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…

Mathematical Finance · Quantitative Finance 2025-04-15 Elisa Alòs , Eulalia Nualart , Makar Pravosud

We apply vector quantisation within mixed one- and two-factor Bergomi models to implement a fast and efficient approach for option pricing in these models. This allows us to calibrate such models to market data of VIX futures and options.…

Pricing of Securities · Quantitative Finance 2025-07-01 Nelson Kyakutwika , Mesias Alfeus , Erik Schlögl

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

This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To…

Mathematical Finance · Quantitative Finance 2019-09-24 Jaegi Jeon , Geonwoo Kim , Jeonggyu Huh

We propose a model independent framework for generating SPX and VIX risk scenarios based on a joint optimal transport calibration of their market smiles. Starting from the entropic martingale optimal transport formulation of Guyon, we…

Computational Finance · Quantitative Finance 2026-03-20 Charlie Che , Hanxuan Lin , Yudong Yang , Guofan Hu , Lei Fang

In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic…

Mathematical Finance · Quantitative Finance 2025-02-20 Elisa Alòs , Eulalia Nualart , Makar Pravosud

We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough…

Mathematical Finance · Quantitative Finance 2022-10-25 Alessandro Bondi , Sergio Pulido , Simone Scotti

In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility…

Mathematical Finance · Quantitative Finance 2024-03-05 Elisa Alòs , Eulalia Nualart , Makar Pravosud