Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling

Barndorff–Nielsen, Ole E.

doi:10.1111/1467-9469.00045

Cited by 639 publications

(412 citation statements)

References 22 publications

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“…Indeed, the normal-inverse Gaussian reduces to a Gaussian distribution in the case β = 0, α → ∞ and δ/α = σ 2 , where σ is the standard deviation of the Gaussian distribution. 34 Our Table I, leading to 1345 sets of parameters for given combinations of L and D. The values of these parameters for all channels are included as supplementary material, 31 and hopefully provide a compact, useful resource for comparison between theory and experiment.…”

Section: Resultsmentioning

confidence: 99%

Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

Reinhart

Reifenberger

Gupta

et al. 2015

The Journal of Chemical Physics

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We obtained experimental extension data for barcoded E. coli genomic DNA molecules confined in nanochannels from 40 nm to 51 nm in width. The resulting data set consists of 1 627 779 measurements of the distance between fluorescent probes on 25 407 individual molecules. The probability density for the extension between labels is negatively skewed, and the magnitude of the skewness is relatively insensitive to the distance between labels. The two Odijk theories for DNA confinement bracket the mean extension and its variance, consistent with the scaling arguments underlying the theories. We also find that a harmonic approximation to the free energy, obtained directly from the probability density for the distance between barcode labels, leads to substantial quantitative error in the variance of the extension data. These results suggest that a theory for DNA confinement in such channels must account for the anharmonic nature of the free energy as a function of chain extension. C 2015 AIP Publishing LLC. [http://dx

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Section: Resultsmentioning

confidence: 99%

Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

Reinhart

Reifenberger

Gupta

et al. 2015

The Journal of Chemical Physics

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“…In this section, we wish to discuss the precision of these computations. 6 In order to evaluate the algorithm which gives the parameters α and β of the canonical form, we considered a grid covering the range of values of kurtosis from 1.5 to 20. For each value of kurtosis, k, we considered a grid for skewness ranging from 0.1 to √ k − 1 − 0.1.…”

Section: Computation Of the Quartic Exponentialmentioning

confidence: 99%

Fourth order pseudo maximum likelihood methods

Holly

Monfort

Rockinger

2011

Journal of Econometrics

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Please cite this article as: Holly, A., Monfort, A., Rockinger, M., Fourth order pseudo maximum likelihood methods. Journal of Econometrics (2011Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Milovanović for providing a very useful sequence of parameters used for numerical integrations. A C C E P T E D M A N U S C R I P T A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT AbstractWe extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux, Monfort, and Trognon (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed.The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields.Simulation exercises demonstrate the feasibility and robustness of the methods.

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“…This class contains as subclasses the hyperbolic distributions [EK95] by setting λ = 1 and the normal inverse Gaussian distributions [BN97] by setting λ = −1/2. In the latter case, the Lévy measure simplifies to…”

Section: ∂V (Spt) ∂Smentioning

confidence: 99%

Symmetries in Jump-Diffusion Models With Applications in Option Pricing and Credit Risk

Hoogland

Neumann

Vellekoop

2003

Int. J. Theor. Appl. Finan.

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It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of "change of numeraire", but in recent work it was shown that when invoked as a fundamental first principle, it provides a powerful alternative method for the derivation of prices and hedges of derivative securities, when prices of the underlying tradables are driven by Wiener processes. In this article we extend this work to the pricing problem in markets driven not only by Wiener processes but also by Poisson processes, i.e. jump-diffusion models. It is shown that in this case too, the focus on symmetry aspects of the problem leads to important simplifications of, and a deeper insight into the problem. Among the applications of the theory we consider the pricing of stock options in the presence of jumps, and Lévy-processes. Next we show how the same theory, by restricting the number of jumps, can be used to model credit risk, leading to a "market model" of credit risk. Both the traditional Duffie-Singleton and Jarrow-Turnbull models can be described within this framework, but also more general models, which incorporate default correlation in a consistent way. As an application of this theory we look at the pricing of a credit default swap (CDS) and a first-to-default basket option.

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Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling

Cited by 639 publications

References 22 publications

Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

Distribution of distances between DNA barcode labels in nanochannels close to the persistence length

Fourth order pseudo maximum likelihood methods

Symmetries in Jump-Diffusion Models With Applications in Option Pricing and Credit Risk

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