scholarly journals Proximity of Bachelier and Samuelson Models for Different Metrics

2021 ◽  
Vol 9 (3) ◽  
pp. 52-76
Author(s):  
S. Smirnov ◽  
D. Sotnikov
Keyword(s):  
Option Price ◽  
Model Parameters ◽  
European Options ◽  
Probability Metrics ◽  
Lipschitz Continuous ◽  
Oil Market ◽  
Order Of Magnitude ◽  
Kolmogorov Metric ◽  
The Subject ◽  
Probabilistic Metrics

This paper proposes a method of comparing the prices of European options, based on the use of probabilistic metrics, with respect to two models of price dynamics: Bachelier and Samuelson. In contrast to other studies on the subject, we consider two classes of options: European options with a Lipschitz continuous payout function and European options with a bounded payout function. For these classes, the following suitable probability metrics are chosen: the Fortet-Maurier metric, the total variation metric, and the Kolmogorov metric. It is proved that their computation can be reduced to computation of the Lambert in case of the Fortet-Mourier metric, and to the solution of a nonlinear equation in other cases. A statistical estimation of the model parameters in the modern oil market gives the order of magnitude of the error, including the magnitude of sensitivity of the option price, to the change in the volatility.

Investigations of Tail and Defect States in a-Si0.6Ge0.4:H Alloys by PDS and ESR - Implications for the Interaction of Weak and Dangling Bonds

1995 ◽  
Vol 377 ◽  
Author(s):  
Tilo P. Drüsedau ◽  
Andreas N. Panckow ◽  
Bernd Schröder
Keyword(s):  
Silicon Germanium ◽  
Defect Density ◽  
State Density ◽  
Model Parameters ◽  
Defect States ◽  
Conversion Model ◽  
Order Of Magnitude ◽  
Underlying Mechanisms ◽  
Amorphous Silicon Germanium ◽  
Excess Absorption

ABSTRACTInvestigations on the gap state density were performed on a variety of samples of hydrogenated amorphous silicon germanium alloys (Ge fraction around 40 at%) containing different amounts of hydrogen. From subgap absorption measurements the values of the “integrated excess absorption” and the “defect absorption” were determined. Using a calibration constant, which is well established for the determination of the defect density from the integrated excess absorption of a-Si:H and a-Ge:H, it was found that the defect density is underestimated by nearly one order of magnitude. The underlying mechanisms for this discrepancy are discussed. The calibration constants for the present alloys are determined to 8.3×1016 eV−1 cnr2 and 1.7×1016 cm−2 for the excess and defect absorption, respectively. The defect density of the films was found to depend on the Urbach energy according to the law derived from Stutzmann's dangling bond - weak bond conversion model for a-Si:H. However, the model parameters - the density of states at the onset of the exponential tails N*=27×1020 eV−1 cm−3 and the position of the demarcation energy Edb-E*=0.1 eV are considerably smaller than in a-Si:H.

Development of an Inverse Plume Model for Mass Eruption Rate in Unsteady Conditions

2021 ◽  
Author(s):  
Stephen A Solovitz
Keyword(s):  
Laboratory Data ◽  
Model Performance ◽  
Volcanic Eruptions ◽  
Reynolds Numbers ◽  
Model Parameters ◽  
Plume Height ◽  
Eruption Rate ◽  
Mass Eruption Rate ◽  
Downstream Effects ◽  
Order Of Magnitude

Abstract Following volcanic eruptions, forecasters need accurate estimates of mass eruption rate (MER) to appropriately predict the downstream effects. Most analyses use simple correlations or models based on large eruptions at steady conditions, even though many volcanoes feature significant unsteadiness. To address this, a superposition model is developed based on a technique used for spray injection applications, which predicts plume height as a function of the time-varying exit velocity. This model can be inverted, providing estimates of MER using field observations of a plume. The model parameters are optimized using laboratory data for plumes with physically-relevant exit profiles and Reynolds numbers, resulting in predictions that agree to within 10% of measured exit velocities. The model performance is examined using a historic eruption from Stromboli with well-documented unsteadiness, again providing MER estimates of the correct order of magnitude. This method can provide a rapid alternative for real-time forecasting of small, unsteady eruptions.

scholarly journals A Bayesian ensemble data assimilation to constrain model parameters and land-use carbon emissions

2018 ◽  
Vol 15 (9) ◽  
pp. 2909-2930 ◽  
Author(s):  
Sebastian Lienert ◽  
Fortunat Joos
Keyword(s):  
Land Use ◽  
Carbon Emissions ◽  
Latin Hypercube Sampling ◽  
Historical Period ◽  
Model Parameters ◽  
Dynamic Global Vegetation Model ◽  
Order Of Magnitude ◽  
The Difference ◽  
Wood Harvest ◽  
Global Vegetation

Abstract. A dynamic global vegetation model (DGVM) is applied in a probabilistic framework and benchmarking system to constrain uncertain model parameters by observations and to quantify carbon emissions from land-use and land-cover change (LULCC). Processes featured in DGVMs include parameters which are prone to substantial uncertainty. To cope with these uncertainties Latin hypercube sampling (LHS) is used to create a 1000-member perturbed parameter ensemble, which is then evaluated with a diverse set of global and spatiotemporally resolved observational constraints. We discuss the performance of the constrained ensemble and use it to formulate a new best-guess version of the model (LPX-Bern v1.4). The observationally constrained ensemble is used to investigate historical emissions due to LULCC (ELUC) and their sensitivity to model parametrization. We find a global ELUC estimate of 158 (108, 211) PgC (median and 90 % confidence interval) between 1800 and 2016. We compare ELUC to other estimates both globally and regionally. Spatial patterns are investigated and estimates of ELUC of the 10 countries with the largest contribution to the flux over the historical period are reported. We consider model versions with and without additional land-use processes (shifting cultivation and wood harvest) and find that the difference in global ELUC is on the same order of magnitude as parameter-induced uncertainty and in some cases could potentially even be offset with appropriate parameter choice.

Radial heat and water transport across the airway wall

1990 ◽  
Vol 69 (1) ◽  
pp. 222-231 ◽  
Author(s):  
C. L. Tsai ◽  
G. M. Saidel ◽  
E. R. McFadden ◽  
J. M. Fouke
Keyword(s):  
Initial Conditions ◽  
Variable Parameter ◽  
Blood Perfusion ◽  
Breath Hold ◽  
Model Parameters ◽  
Airway Wall ◽  
Healthy Human ◽  
Asthmatic Patients ◽  
Order Of Magnitude ◽  
The Difference

The thermal profiles in the airways of healthy human volunteers and patients with asthma differ after cessation of hyperpnea. The asthmatic patients rewarm their airways more rapidly. To identify thermal properties and processes that could account for the difference between these populations, we developed a model describing the radial transport of heat and water across the trachea. A distinctive feature of the model is a variable parameter describing blood supply to the mucosal and submucosal layers. Simulations performed with the model are initiated by a breath-hold maneuver and are propagative in time. Blood perfusion rates in the airway wall, the thickness of the layer of airway surface liquid, and the mucosa-submucosa thickness, all thought to be more pronounced in asthmatic patients, were varied by changing model parameters and initial conditions. Increasing the thickness of the liquid layer by more than an order of magnitude had little effect on the temperature or water content in the airway lumen. Doubling the blood flow to the mucosa-submucosa resulted in a slight increase in airway temperature. When this effect was coupled, however, with an increase in the thickness of the mucosa-submucosa layer, the increase in temperature was more pronounced. Because the bronchial circulation is the major source of heat to the airway, these results indicate that differences in airway wall thickness coupled with differences in the magnitude or responsiveness of the bronchial microcirculation could account for the differences in intra-airway temperature between the two populations.

On regularized distance and related functions

1979 ◽  
Vol 83 (1-2) ◽  
pp. 115-122 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Continuous Function ◽  
Closed Subset ◽  
Parameter Family ◽  
Lipschitz Continuous Function ◽  
Partial Derivatives ◽  
Lipschitz Continuous ◽  
Order Of Magnitude ◽  
Derivatives Of ◽  
Smooth Approximations

SynopsisLetFbe any closed subset of ℝN. Stein's regularized distance is a smooth (C∞) function, defined on the complementcF, that approximates the distance fromFof any pointx ∈cFin the manner shown by the inequalities (*) in the Introduction below. In this paper we use a method different from Stein's to construct a one-parameter family of smooth approximations to any positive Lipschitz continuous function, with the effect that the constants in (*) can be made arbitrarily close to 1. It is shown that partial derivatives of order two or more, while necessarily unbounded, are best possible in order of magnitude.

Game Theoretical Approach to Model Decision Making for Merging Maneuvers at Freeway On-Ramps

2017 ◽  
Vol 2623 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Kyungwon Kang ◽  
Hesham A. Rakha
Keyword(s):  
Decision Making ◽  
Theoretical Approach ◽  
Model Parameters ◽  
Decision Making Process ◽  
Optimization Approach ◽  
Data Set ◽  
Deliberation Process ◽  
Proposed Model ◽  
Game Theoretical Approach ◽  
The Subject

Drivers of merging vehicles decide when to merge by considering surrounding vehicles in adjacent lanes in their deliberation process. Conflicts between drivers of the subject vehicles (i.e., merging vehicles) in an auxiliary lane and lag vehicles in the adjacent lane are typical near freeway on-ramps. This paper models a decision-making process for merging maneuvers that uses a game theoretical approach. The proposed model is based on the noncooperative decision making of two players, that is, drivers of the subject and lag vehicles, without consideration of advanced communication technologies. In the decision-making process, the drivers of the subject vehicles elect to accept gaps, and drivers of lag vehicles either yield or block the action of the subject vehicle. Corresponding payoff functions for two players were formulated to describe their respective maneuvers. To estimate model parameters, a bi-level optimization approach was used. The next generation simulation data set was used for model calibration and validation. The data set defined the moment the game started and was modeled as a continuous sequence of games until a decision is made. The defined merging decision-making model was then validated with an independent data set. The validation results reveal that the proposed model provides considerable prediction accuracy with correct predictions 84% of the time.

scholarly journals Sudakov Form Factors in Leptoproduction of Vector Mesons

1997 ◽  
Vol 12 (35) ◽  
pp. 2717-2723
Author(s):  
I. M. Dremin
Keyword(s):  
Cross Section ◽  
Form Factors ◽  
Model Parameters ◽  
Vector Mesons ◽  
Large Size ◽  
Color Dipole ◽  
Order Of Magnitude ◽  
The Cross ◽  
Qcd Inspired Model

It is shown that Sudakov form factors for a color dipole in a QCD-inspired model of leptoproduction of vector mesons reduce the value of the cross-section of the process by an order of magnitude. They suppress the large size quark–antiquark pairs and unequal sharing of energy among the components of the dipole. Some freedom in the choice of the model parameters is also discussed.

scholarly journals Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-16
Author(s):  
Raúl Merino ◽  
Josep Vives
Keyword(s):  
Implied Volatility ◽  
Option Price ◽  
Model Parameters ◽  
Numerical Comparison ◽  
Cev Model ◽  
Volatility Models ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Volatility Surface ◽  
Price Decomposition

We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.

scholarly journals ANALYSIS OF THE SENSITIVITY OF VISCOELASTIC PARAMETERS AT THE STRAIN-RATE OF A THERMOPLASTIC

2019 ◽  
Author(s):  
Younès Saadallah ◽  
Semcheddine Derfouf ◽  
Belhi Guerira
Keyword(s):  
Strain Rate ◽  
Mathematical Formulation ◽  
Tensile Tests ◽  
Polyamide 6 ◽  
Model Parameters ◽  
Behavior Model ◽  
Strain Rates ◽  
Exponential Regression ◽  
Viscoelastic Parameters ◽  
The Subject

The behavior of thermoplastics depends on several factors, mainly time and temperature. The present work is the subject of a study of the dependence of these materials on time. The material considered in this study is a polyamide 6. The applied behavior model is represented by the Kelvin-Voigt viscoelastic mechanism with instant elasticity. Following the mathematical formulation of the equations of the model, tensile tests at different strain rates are conducted. The model parameters are then identified. These being sensitive to the strain-rate, the relation which links them with it is established by means of an exponential regression. The experimental results and those obtained by the model are presented, compared and interpreted. Their relevance and coherence validates both the model and the approach adopted.

scholarly journals Quantifying the effect of ocean bed properties on ice sheet geometry over 40 000 years with a full-Stokes model

2020 ◽  
Vol 14 (11) ◽  
pp. 3917-3934
Author(s):  
Clemens Schannwell ◽  
Reinhard Drews ◽  
Todd A. Ehlers ◽  
Olaf Eisen ◽  
Christoph Mayer ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Ice Sheet ◽  
Time Frame ◽  
Model Parameters ◽  
Glacial Cycle ◽  
Ice Shelf ◽  
Glacial Cycles ◽  
Sediment Redistribution ◽  
Grounding Line ◽  
Order Of Magnitude

Abstract. Simulations of ice sheet evolution over glacial cycles require integration of observational constraints using ensemble studies with fast ice sheet models. These include physical parameterisations with uncertainties, for example, relating to grounding-line migration. More complete ice dynamic models are slow and have thus far only be applied for < 1000 years, leaving many model parameters unconstrained. Here we apply a 3D thermomechanically coupled full-Stokes ice sheet model to the Ekström Ice Shelf embayment, East Antarctica, over a full glacial cycle (40 000 years). We test the model response to differing ocean bed properties that provide an envelope of potential ocean substrates seawards of today's grounding line. The end-member scenarios include a hard, high-friction ocean bed and a soft, low-friction ocean bed. We find that predicted ice volumes differ by > 50 % under almost equal forcing. Grounding-line positions differ by up to 49 km, show significant hysteresis, and migrate non-steadily in both scenarios with long quiescent phases disrupted by leaps of rapid migration. The simulations quantify the evolution of two different ice sheet geometries (namely thick and slow vs. thin and fast), triggered by the variable grounding-line migration over the differing ocean beds. Our study extends the timescales of 3D full-Stokes by an order of magnitude compared to previous studies with the help of parallelisation. The extended time frame for full-Stokes models is a first step towards better understanding other processes such as erosion and sediment redistribution in the ice shelf cavity impacting the entire catchment geometry.

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