Volatility is rough

By Jim Gatheral, Thibault Jaisson, Mathieu Rosenbaum. 2014

874 citations recorded by the source corpus.

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault [Long memory in continuous-time stochastic volatility models. Math. Finance, 1998, 8(4), 291–323]. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, . We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not a long memory process in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/ef8382b7dcd1436a130ea54acb399b9bb8787fd3

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Citations in the corpus

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.”
Statistical inference for Vasicek-type model driven by Hermite processes (2017, background): “The paper [11] on rough volatility contends that the short-time behavior indicates that the Hurst parameter H of volatility is less than 1 2 .”
Rough volatility: Evidence from option prices (2017, methodology): “Our main result is a confirmation of that in [13]: When using alternate spot volatility measurement methods based on option prices, we can still conclude that volatility is rough.”
Rough Volatility: Fact or Artefact? (2022, positive): “However, in an interesting simulation study using paths (2018) using SPX 5-minute realized volatility from the Oxford-Man Institute’s Realized Library.”
No‐arbitrage implies power‐law market impact and rough volatility (2018, background): “This stylized fact first established in [15] and confirmed in [4, 24] means that the (log-)volatility process of an asset essentially behaves as a fractional Brownian motion (fBm for short) with Hurst parameter of order 0.”
Markovian structure of the Volterra Heston model (2018, methodology): “It has been introduced in [2] for the purpose of financial modeling following the literature on so-called rough volatility models [10].”
A weak solution theory for stochastic Volterra equations of convolution type (2019, background): “, 2013), and rough volatility modeling in finance (El Euch and Rosenbaum, 2019; Gatheral et al., 2018).”
Short-time at-the-money skew and rough fractional volatility (2015, methodology): “Further, it has been reported that the slope around at the money obeys a power law with respect to the time to maturity: see Alòs et al. (2007), Fouque et al. (2004), Gatheral et al. (2014).”
Lifting the Heston model (2018, methodology): “Recently, rough volatility models have been introduced as a fresh substitute with remarkable fits of the implied volatility surface, see [5, 19, 26].”
Pricing under rough volatility (2015, positive): “SPX variance curve forecasts are formed using the predictor (8.1) from the time series of daily realized variance estimates from same Oxford-Man data-set that was used in Gatheral et al. (2014).”
Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case (2018, background): “monstrate that in this Markovian light the theory of stochastic Volterra processes becomes almost classical. 1. Introduction In the realm of the recent discovery of rough volatility models (see e.g., [4, 21, 15, 16]), stochastic Volterra processes have been studied extensively, for instance in [24, ”
A regularity structure for rough volatility (2017, methodology): “(f of exponential form; [27]) By an easy localization argument one shows that for f smooth (but without any further bounds) ones still has”
Short-time near-the-money skew in rough fractional volatility models (2017, background): “Email: friz@math.tu-berlin.de, P.K.Friz@gmail.com markets both from a statistical (Gatheral et al. 2014; Bennedsen et al. 2016) and an option-pricing point of view (Bayer et al. 2016).”
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes (2015, result): “Coming back to financial applications, this means that in practice, the volatility process should be very irregular, which is perfectly in line with the recent empirical measures of the volatility smoothness obtained in [18].”
ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL (2018, background): “This extension is important in light of the empirical results in Gatheral et al. (2018). Following Xiao and Yu (2018), we assume the whole trajectory ofXt for t ∈ [0, T ] is available.”
Discretely sampled signals and the rough Hoff process (2013, methodology): “For example, momentum trading and long-range dependence may be better captured in a nonsemimartingale context by modelling volatility using fractional Brownian motion with a Hurst parameter H 6= 1 2 ([1, 4, 12]).”
The characteristic function of rough Heston models (2016, methodology): “Beyond moments, it is also established in Gatheral et al. (2018) that the empirical correlation structure of volatility is very well reproduced when using rough fractional volatility models.”
The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, methodology): “To circumvent this issue, it is then natural to think of rough volatility models as recently introduced in [18].”