Pricing under rough volatility

Bayer, Christian; Friz, Peter K.; Gatheral, Jim

doi:10.1080/14697688.2015.1099717

Cited by 372 publications

(463 citation statements)

References 12 publications

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“…We also did not perform analyses of models with time dependent parameters which were studied by Mikhailov and Nögel (2003), Osajima (2007), Elices (2008), Benhamou, Gobet, and Miri (2010) etc. As mentioned in Bayer, Friz, and Gatheral (2016), the general overall shape of the volatility surface, with respect to equities, does not change in time significantly.…”

Section: Stochastic Volatility Modelsmentioning

confidence: 66%

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

2018

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In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the jump part in the underlying model dynamics. Also an impact of the long memory parameter is measured for the approximative fractional SV model. For the first time, the robustness of calibrated models is measured using bootstrapping methods on market data and Monte-Carlo filtering techniques. In contrast to several other sensitivity analysis approaches for SV models, the newly proposed methodology does not require independence of calibrated parameters -an assumption that is typically not satisfied in practice. Empirical study is performed on data sets of Apple Inc. equity options traded in April and May 2015.

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Section: Stochastic Volatility Modelsmentioning

confidence: 66%

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

2018

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“…A model with piece-wise constant parameters is studied by Mikhailov and Nögel [10], a linear time dependent Heston model is studied by Elices [45] and a more general case is introduced by Benhamou et al [46], who calculate also an approximation to the option price. However, Bayer, Fritz and Gatheral [47] claim that the overall shape of the volatility surface does not change in time and that also the parameters should remain constant. Affine jump-diffusion processes keep original parameters constant and add jumps to the underlying asset process, to volatility or to both, see e.g paper by Duffie, Pan and Singleton [48].…”

Section: Resultsmentioning

confidence: 99%

Calibration and simulation of Heston model

Mrázek

Pospı́šil

2017

Open Mathematics

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Abstract:We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods.We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact scheme, IJK) we introduce also a new method combining the Exact approach and Milstein (E+M) scheme. Test is carried out by pricing European call options by Monte Carlo method. Presented comparisons give an empirical evidence and recommendations what methods should and should not be used and why. We further improve the QE scheme by adapting the antithetic variates technique for variance reduction.

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“…The R‐L FBM has recently been used to define the rough Bergomi model to study stochastic volatility in Bayer et al. ().…”

Section: New Classes Of Nonstationary Self‐similar Gaussian Processesmentioning

confidence: 99%

“…The shot noise processes can be used to model limit order books for very-or ultra-high-frequency data. On the other hand, FBM has been used in portfolio optimization with transaction costs (Czichowsky, Peyre, Schachermayer, & Yang, 2018;Schachermayer, 2017) and rough stochastic volatility (Bayer, Friz, & Gatheral, 2016). It would be interesting to see how one can use the generalized FBM in these studies.…”

Section: Literature Reviewmentioning

confidence: 99%

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Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion

Pang

Taqqu

2019

High Frequency

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We study shot noise processes with Poisson arrivals and nonstationary noises. The noises are conditionally independent given the arrival times, but the distribution of each noise does depend on its arrival time. We establish scaling limits for such shot noise processes in two situations: (a) the conditional variance functions of the noises have a power law and (b) the conditional noise distributions are piecewise. In both cases, the limit processes are self‐similar Gaussian with nonstationary increments. Motivated by these processes, we introduce new classes of self‐similar Gaussian processes with nonstationary increments, via the time‐domain integral representation, which are natural generalizations of fractional Brownian motions.

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Pricing under rough volatility

Cited by 372 publications

References 12 publications

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

Calibration and simulation of Heston model

Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion

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