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Pathwise large deviations for the rough Bergomi model
2018
Journal of Applied Probability
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We investigate some of its probabilistic properties, in particular proving a pathwise large deviations principle for a small-noise version of the model. ...
Introduced recently in mathematical finance by Bayer et al. (2016), the rough Bergomi model has proved particularly efficient to calibrate option markets. ...
In Section 4, we give the proofs of the main results, and Section 5 elucidates the analogous large deviations result for the uncorrelated rough Bergomi model. ...
doi:10.1017/jpr.2018.72
fatcat:bx5scfu4szbphhofeqjcehd7ou
Pathwise large deviations for the rough Bergomi model: Corrigendum
2021
Journal of Applied Probability
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AbstractThis note corrects an error in the definition of the rate function in Jacquier, Pakkanen, and Stone (2018) and slightly simplifies some proofs. ...
To make the estimate work for t = 0, confine ε to the finite interval [0,1] instead of R + in line −4 of p. 1088. ρ in line 4 of p. 1083 and in the proof of [1, Theorem 2.1] on p. 1088. ...
Injectiveness of I follows from the Titchmarsh convolution theorem. We have (I ) * μ = 1 · (·, t)μ(dt) for any measure μ ∈ (C 2 ) * . ...
doi:10.1017/jpr.2020.109
fatcat:xfdzsbzalzcj3gddmokixpoqem
Asymptotics for volatility derivatives in multi-factor rough volatility models
[article]
2020
arXiv
pre-print
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We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. ...
Interestingly, we identify the class of models that generate non-linear smiles around-the-money. ...
Corollary 3.4 can be applied to a large number of existing results on large deviations for (rough) variance processes to get a large deviations result for the integrated (rough) variance process; for example ...
arXiv:1903.02833v3
fatcat:dqk33d3wgngq7dztj443lzsefq
Asymptotics for volatility derivatives in multi-factor rough volatility models
2021
Mathematics and Financial Economics
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AbstractWe study the small-time implied volatility smile for Realised Variance options, and investigate the effect of correlation in multi-factor models on the linearity of the smile. ...
Additionally, we establish small-noise asymptotic behaviour of a general class of VIX options in the large strike regime. ...
The authors are grateful to Antoine Jacquier, Mikko Pakkanen and Ryan McCrickerd for stimulating discussions. AM and HS thank the EPSRC CDT in Financial Computing and Analytics for financial support. ...
doi:10.1007/s11579-020-00288-5
fatcat:cxcji2abq5g3rhkzxgotitkz7u
Large and moderate deviations for stochastic Volterra systems
[article]
2020
arXiv
pre-print
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We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution ...
We show in particular how this framework encompasses most rough volatility models used in mathematical finance and generalises many recent results in the literature. ...
] , while more elaborate pathwise LDPs were derived for the rough Stein-Stein model with random starting point [56] , for the rough Bergomi model [58] , and small-time LDPs for the multifactor rough ...
arXiv:2004.10571v2
fatcat:6lzi7me2xbd3veytlxnq3auws4
Short dated smile under Rough Volatility: asymptotics and numerics
[article]
2021
arXiv
pre-print
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We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. ...
, using the framework [Bayer et al; A regularity structure for rough volatility; Math. ...
A case study: the rough Bergomi model 4.1. The rough Bergomi model. ...
arXiv:2009.08814v2
fatcat:ly44nazctnapnnxndgtoaxn3ay
Precise asymptotics: robust stochastic volatility models
[article]
2020
arXiv
pre-print
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known large deviation asymptotics. ...
When applied to rough volatility models, e.g. in the setting of [Forde-Zhang, Asymptotics for rough stochastic volatility models, 2017], one obtains precise asymptotic for European options which refine ...
Unified large, moderate and rough deviations We now put forward our basic large deviation assumption. ...
arXiv:1811.00267v2
fatcat:4gudex772vbitmx45bgs75hr2u
A regularity structure for rough volatility
[article]
2017
arXiv
pre-print
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and powerful tool to analyze rough volatility models. ...
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 ...
The second set of results concerns large deviations for rough volatility. ...
arXiv:1710.07481v1
fatcat:vzpxkmkcsbftpdugk23wtz3pxe
Rough volatility models: small-time asymptotics and calibration
2020
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We prove a pathwise large deviations principle for a small-noise version of the model, and use this result to establish the small-time behaviour of the rescaled log stock price process. ...
In Chapter 3 we present small-time implied volatility asymptotics for realised variance (RV) options for a number of (rough) stochastic volatility models via a large deviations principle. ...
Corollary 3.2.3 can be applied to a large number of existing results on pathwise large deviations for rough variance processes to get a large deviations result for the integrated rough variance process ...
doi:10.25560/81768
fatcat:mke4gdxdxvgufod3iq5kg5a5xa
Multivariate Stochastic Volatility Models and Large Deviation Principles
[article]
2022
arXiv
pre-print
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2022 pre-print arXiv:2203.09015v1 fatcat:i7oho4fhyfacvoy5lag24qhj2m
The LDP for log-processes is used to obtain large deviation style asymptotic formulas for the distribution function of the first exit time of a log-process from an open set and for the price of a multidimensional ...
We establish a comprehensive sample path large deviation principle (LDP) for log-processes associated with multivariate time-inhomogeneous stochastic volatility models. ...
The previous model is similar in structure to the rough Bergomi model introduced in [3] , and it may be called the super rough Bergomi model. More details can be found in [33] and [4] . ...
arXiv:2203.09015v2
fatcat:bl5svd6kgjg27f4neuun2hpqwm
Large deviations for rough and complete stochastic volatility models
2020
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the (multi-factor) rough Bergomi model for realised variance options. ...
This thesis is concerned with deriving the asymptotic behaviour of these two classes of stochastic volatility models using large deviations techniques, in order to understand the behaviour of the implied ...
Acknowledgments First and foremost, I would like to thank my supervisor, Doctor Antoine Jacquier, whose experience, passion and continuous support guided me through the completion of this thesis. ...
doi:10.25560/82258
fatcat:obk6u34mlnhu3hhaohcwezrghi
A regularity structure for rough volatility
2020
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and powerful tool to analyze rough volatility models. ...
A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. ...
, 1∕2). (5) (Later on, we will allow for explicit time dependence of in order to cover the rough Bergomi model .) ...
doi:10.14279/depositonce-10842
fatcat:wx4ws2uhg5dl3pqh2arwcp66om
Affine and quadratic models for volatility and interest rates markets
2013
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We use a large dataset of S&P 500 and VIX index and option prices with wide ranges of maturities and moneynesses, and analyze the empirical performance of affine jump-diffusion models for S&P 500 returns ...
We analyze the out-of-sample performance of sub-models depending on which products and markets are considered in the in-sample estimation procedure. ...
Markus Leippold, my thesis supervisor, for his support and advice, and for the great work atmosphere I could benefit from. ...
doi:10.5167/uzh-94023
fatcat:mdkgwndfizg5llugfaxbvexcla
Volatility and Correlation Modelling for Equity Indices
2014
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As stated above, we already have pathwise uniqueness for the first n components of the process X. It remains to show it for the remaining components. ...
Even though the process m is more stable than v, the approximation made by the SVJ model of the process m being a constant is too rough. ...
The correlation matrix process C t for the Brownian motions (W 1 , · · · , W n ) defined by the model (1) -(3) -(5) is continuous and almost surely positive definite on any interval [0, T ], for any T ...
doi:10.5167/uzh-108295
fatcat:4gd6gxjclzhuff5e2uyfon6sfa