Calibrating Rough Volatility Models: A Convolutional Neural Network Approach

Stone, Henry W.

doi:10.2139/ssrn.3327135

Cited by 14 publications

(18 citation statements)

References 16 publications

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“…For instance, Hernandez [2017] uses an ANN to calibrate a single-factor Hull-White model. Dimitroff et al [2018], McGhee [2018] and Liu et al [2019a] calibrate stochastic volatility models, and Stone [2019] and Bayer et al [2019] 28 calibrate rough volatility models. Itkin [2019] highlights some pitfalls in the existing approaches and proposes resolutions that improve both performance and accuracy of calibration.…”

Section: Calibrationmentioning

confidence: 99%

Neural Networks for Option Pricing and Hedging: A Literature Review

Ruf

Wang

2019

SSRN Journal

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Neural networks have been used as a nonparametric method for option pricing and hedging since the early 1990s. Far over a hundred papers have been published on this topic. This note intends to provide a comprehensive review. Papers are compared in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Furthermore, related work and regularisation techniques are discussed. Let us explain how to read Table 1. It summarises six relevant characteristics that describe how each paper treats the pricing/hedging problem. The columns 'Features' and 'Outputs' show explanatory featuresWe thank Marc Chataigner, Stéphane Crépey, Antoine Jacquier, and Martin Larsson for comments on an early version of this note. 1 Hahn [2013] also surveys the use of ANNs to predict realised volatility. Here we do not aim to do so.

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Section: Calibrationmentioning

confidence: 99%

Neural Networks for Option Pricing and Hedging: A Literature Review

Ruf

Wang

2019

SSRN Journal

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“…The Hurst index does not only influence the structure of the covariance but also the regularity of the trajectories. Fractional Brownian motion has been used to model a wide range of phenomena such as network traffic [42], stock prices and financial markets [29,40], activity of neurons [10,36], dynamics of the nerve growth [33], fluid dynamics [45], as well as various phenomena in geoscience [23,30,35]. However, the mathematical analysis of stochastic systems involving fBm is a very challenging task.…”

Section: Introductionmentioning

confidence: 99%

Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion

2020

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We analyze the effect of additive fractional noise with Hurst parameter H > 1 2 on fastslow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet, the setting of fractional Brownian motion does not allow us to use the martingale methods from fast-slow systems with Brownian motion. We thoroughly investigate the case where the deterministic system permits a uniformly hyperbolic stable slow manifold. In this setting, we provide a neighborhood, tailored to the fast-slow structure of the system, that contains the process with high probability. We prove this assertion by providing exponential error estimates on the probability that the system leaves this neighborhood. We also illustrate our results in an example arising in climate modeling, where time-correlated noise processes have become of greater relevance recently.

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“…With the notable exception of the rough Heston model [1,26,27,25,24] and its affine extensions [2,35], the absence of Markovianity of the fractional Brownian motion prevents any pricing tools other than Monte Carlo simulations; the simulation of continuous Gaussian processes, including fractional Brownian motion, is traditionally slow as soon as one steps away from the standard Brownian motion. However, the clear superiority-for estimation and calibration-of these rough volatility models has encouraged deep and fast innovations in numerical methods for pricing, in particular the now standard Hybrid scheme [10,43] as well as Donsker-type theorems [45,64], numerical approximations [6,42,36] and machine learning-based techniques [47,71].…”

Section: Introductionmentioning

confidence: 99%