Historical Analysis of Rough Volatility Models to the SPX Market

2020 ◽  
Author(s):  
Sigurd Emil Rømer
Keyword(s):  
Historical Analysis ◽  
Volatility Models ◽  
Rough Volatility

A fast algorithm for simulation of rough volatility models

2021 ◽  
pp. 1-16
Author(s):  
Jingtang Ma ◽  
Haofei Wu
Keyword(s):  
Fast Algorithm ◽  
Volatility Models ◽  
Rough Volatility

scholarly journals Multifactor Approximation of Rough Volatility Models

2019 ◽  
Vol 10 (2) ◽  
pp. 309-349 ◽  
Author(s):  
Eduardo Abi Jaber ◽  
Omar El Euch
Keyword(s):  
Volatility Models ◽  
Rough Volatility

scholarly journals Fractional Riccati Equation and Its Applications to Rough Heston Model

2020 ◽  
Author(s):  
Siow W. Jeng ◽  
Adem Kilicman
Keyword(s):  
Numerical Methods ◽  
Characteristic Function ◽  
Riccati Equation ◽  
Financial Market ◽  
Heston Model ◽  
Short Introduction ◽  
Volatility Models ◽  
Rough Volatility ◽  
Pricing Theory ◽  
Option Pricing Theory

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

scholarly journals Fast Hybrid Schemes for Fractional Riccati Equations (Rough Is Not So Tough)

2020 ◽  
Author(s):  
Giorgia Callegaro ◽  
Martino Grasselli ◽  
Gilles Pagès
Keyword(s):  
Power Series ◽  
Riccati Equations ◽  
Convergence Domain ◽  
Initial Value ◽  
Hybrid Schemes ◽  
Numerical Tests ◽  
Volatility Models ◽  
Rough Volatility ◽  
Log Price ◽  
Complex Coefficients

We solve a family of fractional Riccati equations with constant (possibly complex) coefficients. These equations arise, for example, in fractional Heston stochastic volatility models, which have received great attention in the recent financial literature because of their ability to reproduce a rough volatility behavior. We first consider the case of a zero initial value corresponding to the characteristic function of the log-price. Then we investigate the case of a general starting value associated to a transform also involving the volatility process. The solution to the fractional Riccati equation takes the form of power series, whose convergence domain is typically finite. This naturally suggests a hybrid numerical algorithm to explicitly obtain the solution also beyond the convergence domain of the power series. Numerical tests show that the hybrid algorithm is extremely fast and stable. When applied to option pricing, our method largely outperforms the only available alternative, based on the Adams method.

scholarly journals From microscopic price dynamics to multidimensional rough volatility models

2021 ◽  
Vol 53 (2) ◽  
pp. 425-462
Author(s):  
Mathieu Rosenbaum ◽  
Mehdi Tomas
Keyword(s):  
Price Formation ◽  
Financial Assets ◽  
Correlation Matrices ◽  
Volatility Models ◽  
Microscopic Models ◽  
Joint Dynamics ◽  
Microscopic Features ◽  
Rough Volatility

AbstractRough volatility is a well-established statistical stylized fact of financial assets. This property has led to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that accurately reproduce high-frequency cross-asset interactions and investigate their long-term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion in the multidimensional price formation process. In particular, we recover classical properties of high-dimensional stock correlation matrices.

scholarly journals Volatility Options in Rough Volatility Models

2018 ◽  
Author(s):  
Blanka Horvath ◽  
Antoine Jacquier ◽  
Peter Tankov
Keyword(s):  
Volatility Models ◽  
Rough Volatility

scholarly journals Asymptotic behaviour of randomised fractional volatility models

2019 ◽  
Vol 56 (2) ◽  
pp. 496-523 ◽  
Author(s):  
Blanka Horvath ◽  
Antoine Jacquier ◽  
Chloé Lacombe
Keyword(s):  
Asymptotic Behaviour ◽  
Implied Volatility ◽  
Asymptotic Properties ◽  
Sample Path ◽  
Mathematical Finance ◽  
Small Time ◽  
Small Noise ◽  
Volatility Models ◽  
Rough Volatility ◽  
Sample Path Large Deviations

AbstractWe 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 behaviours in particular). In order to do so, we extend some results on sample path large deviations for such diffusions. As an application, we show how these results characterise the small-time and tail estimates of the implied volatility for rough volatility models, recently proposed in mathematical finance.

Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models

2020 ◽  
Vol 21 (1) ◽  
pp. 11-27
Author(s):  
Blanka Horvath ◽  
Aitor Muguruza ◽  
Mehdi Tomas
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Deep Neural Network ◽  
Volatility Models ◽  
Rough Volatility
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