On an efficient multiple time step Monte Carlo simulation of the SABR model

Leitao, Álvaro; Grzelak, Lech A.; Oosterlee, Cornelis W.

doi:10.1080/14697688.2017.1301676

Cited by 22 publications

(14 citation statements)

References 20 publications

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“…The development of MC simulation methods of the SABR dynamics is relatively recent. While several efficient approximations (Chen, Oosterlee, & VanDerWeide, ; Leitao, Grzelak, & Oosterlee, ,b) have been proposed, an exact simulation method Cai et al () is available for the following three special cases: (a)

ρ = 0

, (b)

β = 0

, and (c)

β = 1

. The key element in this method is to simulate the time‐integrated variance

A_{S}^{[- 1 ∕ 2]}

, conditional on the terminal volatility

Z_{S}

.…”

Section: Models and Preliminariesmentioning

confidence: 99%

Hyperbolic normal stochastic volatility model

Choi

Liu

Seo

2018

Journal of Futures Markets

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For option pricing models and heavy‐tailed distributions, this study proposes a continuous‐time stochastic volatility model based on an arithmetic Brownian motion: a one‐parameter extension of the normal stochastic alpha‐beta‐rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed‐form Monte Carlo simulation scheme and that the transition probability for one special case follows Johnson's SU distribution—a popular heavy‐tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.

show abstract

ρ = 0

, (b)

β = 0

, and (c)

β = 1

. The key element in this method is to simulate the time‐integrated variance

A_{S}^{[- 1 ∕ 2]}

, conditional on the terminal volatility

Z_{S}

.…”

Section: Models and Preliminariesmentioning

confidence: 99%

Hyperbolic normal stochastic volatility model

Choi

Liu

Seo

2018

Journal of Futures Markets

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show abstract

“…Estimating rBergomi model parameters, including the H parameter, is computationally expensive and often relies on the use of Monte Carlo based calibration methods [10,60]. This limits the use of this model in practice despite the benefits it offers [2,19,25].…”

Section: Introductionmentioning

confidence: 99%

Sailing in rough waters: examining volatility of fMRI noise

Leppänen

Stone

Lythgoe

et al. 2020

Preprint

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1.AbstractBackgroundFunctional resonance magnetic imaging (fMRI) noise is usually assumed to have constant volatility. However this assumption has been recently challenged in a few studies examining heteroscedasticity arising from head motion and physiological noise. However, to our knowledge no studies have studied heteroscedasticity in scanner noise. Thus the aim of this study was to estimate the smoothness of fMRI scanner noise using latest methods from the field of financial mathematics.MethodsA multi-echo fMRI scan was performed on a phantom using two 3 tesla MRI units. The echo times were used as intra-time point data to estimate realised volatility. Smoothness of the realised volatility processes is examined by estimating the Hurst parameter, a parameter H ∈ (0, 1) governing the roughness (Hölder continuity) of paths in the rough Bergomi model, introduced in [2]. The rough Bergomi model a member of the family of rough stochastic volatility models. A family of models which was recently popularised in mathematical finance by observations indicating that volatility in financial markets is best described by stochastic models where volatility can be modulated by the Hurst parameter H, which usually calibrates to values H ∈ (0, 0.5) (the rough case), hence inspiring the name of the model family. In this work, calibration of the Hurst parameter H is performed pathwise, using recently developed neural network calibration tools.ResultsIn all experiments the volatility calibrates to values well within the rough case H < 0.5 and on average fMRI scanner noise was very rough with H ≈ 0.03. Substantial variability was also observed, which was caused by edge effects, whereby H was larger near the edges of the phantoms.DiscussionThe findings challenge the assumption that fMRI scanner noise has constant volatility (in fact, the lower the value of H, the more pronounced the oscillations of the volatility, and hence the more “severe” is the violation of the constant volatility assumption) and add to the steady accumulation of studies suggesting implementing methods to model heteroscedasticity may improve fMRI data analysis. Additionally, the present findings add to previous work showing that the mean and normality of fMRI noise processes show edge effects, such that signal near the edges of the images is less likely to meet the assumptions of current modelling methods.

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“…Alternative (non-asymptotic) approaches include the homotopy analysis method (Sakuma, 2019) and partial differential equations (PDEs), see for example Park (2014). There is also recent interest in developing Monte Carlo (MC) simulation schemes for the SABR model, see Song (2013), Leitao et al (2017), and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Full‐fledged SABR Through Markov Chains

Cui¹,

Kirkby²,

Nguyen³

2019

Wilmott

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We present a general purpose technique for the efficient and accurate valuation of options in the shifted stochastic alpha, beta, rho (shifted‐SABR) model which includes SABR as a special case. The method is based on a novel double‐layer continuous‐time Markov chain from which closed form matrix expressions for European options are derived. We also propose a recursive risk‐neutral valuation technique for pricing discretely monitored path‐dependent options, and use it to price Bermudian and barrier options. In addition, we provide single Laplace transform formulae for discretely monitored arithmetic Asian options. Numerical experiments confirm the accuracy and efficiency of the proposed method, which is suitable for practical use.

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On an efficient multiple time step Monte Carlo simulation of the SABR model

Cited by 22 publications

References 20 publications

Hyperbolic normal stochastic volatility model

Hyperbolic normal stochastic volatility model

Sailing in rough waters: examining volatility of fMRI noise

Full‐fledged SABR Through Markov Chains

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