Pathwise large deviations for the rough Bergomi model

Jacquier, Antoine; Pakkanen, Mikko S.; Stone, Henry W.

doi:10.1017/jpr.2018.72

Cited by 47 publications

(48 citation statements)

References 45 publications

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“…Remark 3.1. The process log v has a modification whose sample paths are almost surely locally γ-Hölder continuous, for all γ ∈ 0, α + 1 2 [Jacquier et al 2018, Proposition 2.2]. As stated above, the fBm has sample paths that are γ-Hölder continuous for any γ ∈ (0, H) [Biagini et al 2008, Theorem 1.6.1], so that the rBergomi model also captures this "roughness" by identification α = H − 1/2.…”

Section: Methodsmentioning

confidence: 99%

Calibrating Rough Volatility Models: A Convolutional Neural Network Approach

Stone

2019

SSRN Journal

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Section: Methodsmentioning

confidence: 99%

Calibrating Rough Volatility Models: A Convolutional Neural Network Approach

Stone

2019

SSRN Journal

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“…Proof of Proposition 5.2. The proof of Proposition 5.2, which is similar to the proofs given in [JPS18], is made up of three parts. The first part is to prove that H g,T , ·, · H g,T is a separable Hilbert…”

Section: Bergomi Modelmentioning

confidence: 97%

Asymptotics for Volatility Derivatives in Multi-Factor Rough Volatility Models

2019

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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. We provide numerical results along with efficient and robust numerical recipes to compute the rate function; the backbone of our theoretical framework. Based on our results, we further develop approximation schemes for the density of RV, which in turn allows to express the volatility swap in close-form. Lastly, we investigate different constructions of multi-factor models and how each of them affects the convexity of the implied volatility smile. Interestingly, we identify the class of models that generate non-linear smiles around-the-money.Date: March 25, 2019.2010 Mathematics Subject Classification. Primary 60F10, 60G22; Secondary 91G20, 60G15, 91G60. ε > 0, P ε is the joint law and, for each δ > 0, the set ω :and lim sup ε↓0 h ε log P ε (Γ δ ) = −∞, where Γ δ := {(ỹ, y) : d(ỹ, y) > δ} ⊂ Y × Y. Theorem D.2. Let X and Y be topological spaces and f : X → Y a continuous function. Consider a good rate function I : X → [0, ∞]. For each y ∈ Y, define I (y) := inf{I(x) : x ∈ X , y = f (x)}. Then, if I controls the LDP associated with a family of probability measures {µ ε } on X , the I controls the LDP associated with the family of probability measures {µ ε • f −1 } on Y and I is a good rate function on Y.

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“…We assume that the mean reversion κ, the Hurst parameter H and the initial volatility V 0 are given, while the volatility of volatility ν, the correlation ρ and the long-term variance level V ∞ need to be calibrated. The reason for this choice is practical (the dimension of the optimisation problem is reduced), but can be easily justified: a good proxy for the initial variance V 0 is given by the short-term at-the-money smile, and the Hurst parameter can be calibrated by the maturity-decay of the at-the-money skew of the implied volatility smile; proper and rigorous explanations, via asymptotic limits and expansions, can be found in [3,9,29,30,37,44,52]. We perform a slice by slice calibration, via a minimisation of the difference between market smiles and of model smiles.…”

Section: Model Calibrationmentioning

confidence: 99%