Volatility Swap Pricing and Variance Swap Pricing under the Mean-Reverting Gaussian Model

2020 ◽  
Vol 66 (10) ◽  
pp. 1-7
Author(s):  
Rui Duan
Keyword(s):  
Gaussian Model ◽  
Variance Swap ◽  
The Mean

Virial expansion for a polymer chain: the two parameter approximation

1979 ◽  
Vol 367 (1729) ◽  
pp. 143-174 ◽  
Keyword(s):  
Gaussian Model ◽  
Dominant Term ◽  
Cubic Lattices ◽  
Functional Relations ◽  
Ladder Graph ◽  
Simple Rules ◽  
The Mean ◽  
Parameter Approximation ◽  
Ladder Graphs ◽  
Two Parameter

A complete diagrammatic expansion is developed for the Domb-Joyce model of an N -step chain, with an interaction w which varies between 0 and 1. Simple rules are given for obtaining the diagrams. The correspondence between these diagrams and appropriate generating functions permits computation of the coefficients of the series α 2 N ( w ) = 1 + k 1 w + k 2 w 2 + . . ., where α 2 N ( w ) is the expansion factor of the mean square end-to-end length of the chain. The dominant term in N of each of the first three k r is shown to be identical for the three cubic lattices and for the Gaussian continuum model, with the exception of a scale factor h 0 . Retention of only this dominant term yields a ‘two-parameter’ expansion equivalent to that of Zimm (1946), Fixman (1955) and others. Diagrams are classed either as ladder or as non-ladder graphs. The ladder graph contributions are summed by using functional relations of Domb & Joyce (1972). The non-ladder contributions for the first three coefficients are computed individually, thereby yielding results for k 1 , k 2 and k 3 in terms of the ‘universal’ parameter z = h 0 N 1/2 w . The terms k 1 and k 2 agree with previous computations for the Gaussian model but k 3 differs slightly.

scholarly journals Optimal Model Mapping for Intravoxel Incoherent Motion MRI

2021 ◽  
Vol 15 ◽  
Author(s):  
Yen-Peng Liao ◽  
Shin-ichi Urayama ◽  
Tadashi Isa ◽  
Hidenao Fukuyama
Keyword(s):  
Diffusion Model ◽  
Gaussian Model ◽  
Mapping Method ◽  
Intravoxel Incoherent Motion ◽  
Optimal Model ◽  
Gamma Model ◽  
Additional Information ◽  
Perfusion Fraction ◽  
Model Mapping ◽  
The Mean

In general, only one diffusion model would be applied to whole field-of-view voxels in the intravoxel incoherent motion-magnetic resonance imaging (IVIM-MRI) study. However, the choice of the applied diffusion model can significantly influence the estimated diffusion parameters. The quality of the diffusion analysis can influence the reliability of the perfusion analysis. This study proposed an optimal model mapping method to improve the reliability of the perfusion parameter estimation in the IVIM study. Six healthy volunteers (five males and one female; average age of 38.3 ± 7.5 years). Volunteers were examined using a 3.0 Tesla scanner. IVIM-MRI of the brain was applied at 17 b-values ranging from 0 to 2,500 s/mm2. The Gaussian model, the Kurtosis model, and the Gamma model were found to be optimal for the CSF, white matter (WM), and gray matter (GM), respectively. In the mean perfusion fraction (fp) analysis, the GM/WM ratios were 1.16 (Gaussian model), 1.80 (Kurtosis model), 1.94 (Gamma model), and 1.54 (Optimal model mapping); in the mean pseudo diffusion coefficient (D*) analysis, the GM/WM ratios were 1.18 (Gaussian model), 1.19 (Kurtosis model), 1.56 (Gamma model), and 1.24 (Optimal model mapping). With the optimal model mapping method, the estimated fp and D* were reliable compared with the conventional methods. In addition, the optimal model maps, the associated products of this method, may provide additional information for clinical diagnosis.

Closure Approximations for PDF Equations Based on the Simonin-Deutsch-Minier (SDM) Equation for Gas-Particle Flows

2003 ◽  
Author(s):  
Michael W. Reeks
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Gaussian Model ◽  
Convection Term ◽  
Langevin Model ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Particle Flows ◽  
Closure Approximations ◽  
The Mean

The paper addresses an apparent incompatibility between the two current formulations of the PDF approach for the dispersion of particles in a uniform shear flow. It is shown that this incompatibility arises through neglect of the inertial convection term in the transport equation for the mean carrier flow velocity local to a particle. Evaluating this term for a Gaussian process gives identical results for both formulations. This also resolves a long standing incompatibility in previous forms for the fluid point diffusions coefficients in a simple shear. A closure approximation is given based on a Gaussian model for the contribution due to the fluctuating shear which has previously been assumed to be white noise in the generalised Langevin model (GLM) due to Simonin, Deutsch and Minier.

scholarly journals Revisiting Mean Flow and Mixing Properties of Negatively Round Buoyant Jets Using the Escaping Mass Approach (EMA)

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 131
Author(s):  
Aristeidis A. Bloutsos ◽  
Panayotis C. Yannopoulos
Keyword(s):  
Numerical Models ◽  
Gaussian Model ◽  
Uniform Density ◽  
Mean Flow ◽  
Buoyant Jet ◽  
Buoyant Jets ◽  
Mixing Properties ◽  
Flow Phenomena ◽  
The Mean ◽  
Return Point

The flow formed by the discharge of inclined turbulent negatively round buoyant jets is common in environmental flow phenomena, especially in the case of brine disposal. The prediction of the mean flow and mixing properties of such flows is based on integral models, experimental results and, recently, on numerical modeling. This paper presents the results of mean flow and mixing characteristics using the escaping mass approach (EMA), a Gaussian model that simulates the escaping masses from the main buoyant jet flow. The EMA model was applied for dense discharge at a quiescent ambient of uniform density for initial discharge inclinations from 15° to 75°, with respect to the horizontal plane. The variations of the dimensionless terminal centerline and the external edge’s height, the horizontal location of the centerline terminal height, the horizontal location of centerline and the external edge’s return point as a function of initial inclination angle are estimated via the EMA model, and compared to available experimental data and other integral or numerical models. Additionally, the same procedure was followed for axial dilutions at the centerline terminal height and return point. The performance of EMA is acceptable for research purposes, and the simplicity and speed of calculations makes it competitive for design and environmental assessment studies.

A multivariate multilevel Gaussian model with a mixed effects structure in the mean and covariance part

2013 ◽  
Vol 33 (11) ◽  
pp. 1877-1899 ◽  
Author(s):  
Baoyue Li ◽  
Luk Bruyneel ◽  
Emmanuel Lesaffre
Keyword(s):  
Gaussian Model ◽  
Mixed Effects ◽  
The Mean

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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