Nonparametric Bayesian Volatility Estimation

Gugushvili, Shota; Meulen, Frank van der; Schauer, Moritz; Spreij, Peter

doi:10.1007/978-3-030-04161-8_19

Cited by 8 publications

(12 citation statements)

References 63 publications

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“…This is indeed the case for the technique we study in this work. Our prior specification and a deliberate, but asymptotically harmless misspecification of the drift by taking b ≡ 0 are clever choices which enable to combine our earlier work in Gugushvili et al [2018a] with FFBS algorithm for Gaussian linear state space models. This directly gives a conceptually simple algorithm (Gibbs sampler) to obtain samples from the posterior, from which measures of inferential uncertainty can be extracted in a straightforward way.…”

Section: Discussionmentioning

confidence: 99%

“…Over short time intervals [t i−1 , t i ], the term ti ti−1 s(t)dW t in (3), roughly speaking, will dominate the term ti ti−1 b(t, X t )dt, as the former scales as ∆t i , whereas the latter as √ ∆t i (due to the properties of the Wiener process paths). As our emphasis is on learning s rather than b, following Gugushvili et al [2017], Gugushvili et al [2018a] we act as if the process X had a zero drift, b ≡ 0. A similar idea is often used in frequentist volatility estimation procedures in the high frequency financial data setting; see Mykland and Zhang [2012], Section 2.1.5 for an intuitive exposition.…”

Section: Methodsmentioning

confidence: 99%

“…For the measurement error variance η v , we assume a priori η v ∼ IG(α v , β v ). The construction of the prior for s is more complex and follows Gugushvili et al [2018a], that in turn relies on Cemgil and Dikmen [2007]. Fix an integer m < n. Then we have a unique decomposition n = mN + r with 0 ≤ r < m, where…”

Section: Methodsmentioning

confidence: 99%

“…We also endow α with a prior distribution and assume log α ∼ N (a, b), with hyperparameters a ∈ R, b > 0 chosen so as to render the hyperprior on α diffuse. As explained in Gugushvili et al [2017], Gugushvili et al [2018a], the hyperparameter N (or equivalently m) can be considered both as a smoothing parameter and the resolution at which one wants to learn the volatility function. Obviously, given the limited amount of data, this resolution cannot be made arbitrarily fine.…”

Section: Methodsmentioning

confidence: 99%

“…Obviously, given the limited amount of data, this resolution cannot be made arbitrarily fine. On the other hand, as shown in Gugushvili et al [2018a] (see also Gugushvili et al [2018b]), inference with the IGMC prior is quite robust with respect to a wide range of values of N , as the corresponding Bayesian procedure has an additional regularisation parameter α that is learned from the data. Statistical optimality results in Munk and Schmidt-Hieber [2010] suggest that in our setting N should be chosen considerably smaller than in the case of an SDE observed without noise (that was studied via the IGMC prior in Gugushvili et al [2018a]).…”

Section: Methodsmentioning

confidence: 99%

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Nonparametric Bayesian Volatility Learning Under Microstructure Noise

et al. 2018

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Aiming at financial applications, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesian approach, where we model the volatility function a priori as piecewise constant. Its prior is specified via the inverse Gamma Markov chain. Sampling from the posterior is accomplished by incorporating the Forward Filtering Backward Simulation algorithm in the Gibbs sampler. Good performance of the method is demonstrated on two representative synthetic data examples. Finally, we apply the method on the EUR/USD exchange rate dataset.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Nonparametric Bayesian Volatility Learning Under Microstructure Noise

et al. 2018

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Nonparametric Bayesian volatility learning under microstructure noise

Gugushvili

Meulen

Schauer

et al. 2022

Jpn J Stat Data Sci

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Bayesian wavelet de-noising with the caravan prior

et al. 2019

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According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes denoising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.

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Nonparametric Bayesian Volatility Estimation

Cited by 8 publications

References 63 publications

Nonparametric Bayesian Volatility Learning Under Microstructure Noise

Nonparametric Bayesian Volatility Learning Under Microstructure Noise

Nonparametric Bayesian volatility learning under microstructure noise

Bayesian wavelet de-noising with the caravan prior

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