Pricing under rough volatility

By Christian Bayer, Peter K. Friz, Jim Gatheral. 2015

509 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/13fc9e654d4509fa9264d7c9e7216121bccf1707

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Citations in the corpus

Affine Volterra processes (2017, methodology): “uctuates more rapidly than Brownian motion, which is inconsistent with standard semimartingale aﬃne models. Fractional volatility modelssuch as those byGuennoun et al. (2017); Gatheral et al. (2014); Bayer et al. (2016); El Euch and Rosenbaum (2016); Bennedsen et al. (2016) have emerged as compellin”
Discretely sampled signals and the rough Hoff process (2013, methodology): “In the case of x ∈ C ( [0, 1],R ) where p ∈ [1, 2), the iterated integrals of x are canonically defined via Young integration [31].”
On VIX futures in the rough Bergomi model (2017, methodology): “Finally, and most importantly, we follow the recent paper by Bayer et al. (2015), in order to extend the RFSV model to pricing schemes under the measure Q.”
A regularity structure for rough volatility (2017, methodology): “We choose f(x, t) = exp(x) because this closely resembles the rough Bergomi model (see [4] and below).”
The characteristic function of rough Heston models (2016, methodology): “In particular, contrary to most stochastic volatility models, rough volatility models generate an exploding term structure for the at-the-money skew when maturity goes to zero, which is very commonly observed in practice; see Bayer, Friz, and Gatheral (2016), Gatheral et al. (2018), and Section 5.”
Perfect hedging in rough Heston models (2017, background): “However, the interest of having a pricing (1)In fact this has been clearly established in [4, 12] for the so-called rough Bergomi model, where the logvolatility follows a fractional Brownian motion.”
A martingale approach for fractional Brownian motions and related path dependent PDEs (2017, methodology): “We note again that a wide range of volatility options are available in the financial market, at least for the S&P 500: see the VIX options in Gatheral [23].”
Decoupling the Short- and Long-Term Behavior of Stochastic Volatility (2016, unknown): “allycompute the covariance structure of the Gaussianbivariateprocess (B;X) and simulate Band Xjointly, and in this way account for correlation between the two processes. This was the approach taken inBayer et al. (2016). However, as the authors also note, the Cholesky factorization iscomputationally”
Short-time at-the-money skew and rough fractional volatility (2015, methodology): “Recently, independently of this work, Bayer et al. (2015) constructed a timeconsistent model by a different approach.”
Short-time near-the-money skew in rough fractional volatility models (2017, methodology): “† Note that expressions for the exact same scenario have have been computed before in the original pricing paper (Bayer et al. 2016), yet in that version the expression for the autocorrelation of the fBM B̂ was incorrect.”
Rough volatility: Evidence from option prices (2017, background): “In particular, the exploding term structure when maturity goes to zero of the at-the-money skew (the derivative of the implied volatility with respect to strike) is readily obtained, see Bayer et al. (2016) and Fukasawa (2017). Other developments about rough volatility models can be found in Guennou”
Lifting the Heston model (2018, methodology): “This has been illustrated on real market data in Bayer et al. (2016) and El Euch et al. (2018). Finally, for the sake of completeness, we provide a comparison with the standard Heston model.”
Volatility is rough (2014, unknown): “In Bayer et al. (2016), the authors explore the implications of the RFSV model (written under the physical measure P) for option pricing (under the pricing measure Q).”
ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL (2018, methodology): “(2012); Chronopoulou and Viens (2012a,b); Bayer et al. (2016) and references therein. The model is given by dXt = κ (μ−Xt) dt+ σdB t , (1) where σ is a positive constant, μ, κ ∈ R, H is the Hurst parameter, and B t is an fBm. In a recent study, based on a continuous record of Xt over a time period o”
Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017, unknown): “[7], resolved this problematic of Heston model (i.”
The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, background): “parsimonious models to reproduce all the main stylized facts of historical volatility time series and to fit SPX options smiles, see [4, 14, 18].”