• Industrial Engineering and Management Systems
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• v.9 no.4
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• pp.323-338
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• 2010

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.1
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• pp.3-10
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• 1990

Hull form can be described numerically by two approaches, one is to describe a hull form with a set of curves("curve approach"), and the other is to describe it with surfaces directly("surface approach"). This paper describes the numerical definition scheme of hull form using curve approach method which defines the hull form by a set of curves consisting of 2-dimensional transverse section curves and 3-dimensional longitudinal curves. A set of curves in the hull form definition scheme is described by the modified cubic spline which modified the general parametric cubic spline in order to ensure a very smooth curvature distribution within the curve segment even though a curve segment has large tangent angle at its end points. Illustrative examples are given showing the application of the method to represent the hull form of SWATH ship and oceanographic research vessel. Also, examples for hull form transformation are shown by using this method connected with transformation technique.

• Journal of Environmental Science International
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• v.11 no.9
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.8
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• pp.2561-2571
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• 1996

The flow in the turbomachinery is very unsteady due to the stator-rotor interaction. It has been indicated that the stator-rotor interaction has three distinct causes of unsteadiness: that is, the viscous vortex shedding, wake rotor interaction and potential stator-rotor interaction. In this paper, the mechanism of unsteady potential interaction and wake interaction in the stator-rotor stage flow is numerically investigated in two-dimensional view point. The numerical technique used is the upwind scheme of Van Leer's Flux Vector Splitting(FVS) and cubic spline interpolation is applied on zonal interface. Then, the flow field of a compressor stage composed of NACA 65410 is analyzed. Flow fields are found to be simulated reasonably by this method and the sensitivity due to back-pressure variation is more stronger than rotor-velocity variation.

• Economic and Environmental Geology
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• v.25 no.1
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• pp.73-77
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• 1992

This paper compares numerical quadrature techniques for computing an inverse Fourier transform integral in two-dimensional resistivity modeling. The quadrature techniques using exponential and cubic spline interpolations are examined for the case of a homogeneous earth model. In both methods the integral over the interval from 0 to ${\lambda}_{min}$, where ${\lambda}_{min}$, is the minimum sampling spatial wavenumber, is calculated by approximating Fourier transformed potentials to a logarithmic function. This scheme greatly reduces the inverse Fourier transform error associated with the logarithmic discontinuity at ${\lambda}=0$. Numrical results show that, if the sampling intervals are adequate, the cubic spline interpolation method is more accurate than the exponential interpolation method.

• Journal of KIISE:Databases
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• v.31 no.5
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• pp.479-491
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• 2004

Location information of mobile objects is applied to vehicle tracking, digital battlefields, location based services, and telematics. Their location coordinates are periodically measured and stored in the application systems. The linear function is mainly used to estimate the location information that is not in the system at the query time point. However, a new method is needed to improve uncertainties of the location representation, because the location estimation by linear function induces the estimation error. This paper proposes an application method of the cubic spline interpolation in order to reduce deviation of the location estimation by linear function. First, we define location information of the mobile object moving on the two-dimensional space. Next, we apply the cubic spline interpolation to location estimation of the proposed data model and describe algorithm of the estimation operation. Finally, the precision of this estimation operation model is experimented. The experimentation comes out more accurate results than the method by linear function, although the proposed location estimation function uses the small amount of information. The proposed method has an advantage that drops the cost of data storage space and communication for the management of location information of the mobile objects.

• Journal of Mechanical Science and Technology
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• v.14 no.5
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• pp.518-529
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• 2000

A detailed and thorough parametric study of digital image correlation method is presented. A theoretical background and development of the method were introduced and the effects of various parameters on the determination of displacement outputs from the raw original and deformed image information were examined. Use of the normalized correlation coefficient, the use of 20 to 40 pixels for a searching window side, 6 variables searching, bi-cubic spline sub pixel interpolations and the use of coarse-fine search are some of the key choices among the results of parametric studies. The displacement outputs can be further processed with two dimensional curve fitting for the data noise reduction as well as displacement gradient calculation.

• Journal of the Korea Computer Industry Society
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• v.6 no.3
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• pp.495-508
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• 2005

Moving objects are spatiotemporal data that change their location or shape continuously over time. Their location coordinates are periodically measured and stored i3l the application systems. The linear function is mainly used to estimate the location information that is not in the system at the query time point. However, a new method is needed to improve uncertainties of the location representation, because the location estimation by linear function induces the estimation error. This paper proposes an application method of the cubic spline interpolation in order to reduce deviation of the location estimation by linear function. First, we define location information of the moving object on the two-dimensional space. Next, we apply the cubic spline interpolation to location estimation of the proposed data model and describe algorithm of the estimation operation. Finally, the precision of this estimation operation model is experimented. The experimentation comes out more accurate results than the method by linear function.

• Journal of computational fluids engineering
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• v.5 no.2
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• pp.38-46
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• 2000

It has been indicated that the rotor/stator interaction has distinct causes of unsteadiness, such as the viscous vortex shedding, wake/stator interaction and potential rotor/stator interaction. In this paper, the mechanism of unsteady potential interaction in one stage axial compressor is numerically investigated for blade row ratio 1:1 and 2:3 at design point and for blade row ratio 2:3 at off-design point in two-dimensional view point. The numerical technique used is the upwind scheme of Van-Leer's Flux Vector Splitting(FVS) and Cubic spline interpolation is applied on zonal interface. In this study the flow unsteadiness due to potential interaction are found to be larger in blade row ratio 2:3 than in 1:1. The total pressure rise in blade row ratio 2:3 is closer to the real value in design point than that in 1:1. The change of unsteady pressure amplitude according to the variation of stator exit pressure is very small.

• Water for future
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• v.28 no.5
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• pp.151-162
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• 1995

A two-dimensional stream tube dispersion model is developed to simulate accurately transverse dispersion processes of pollutants in natural channels. Two distinct features of the stream tube dispersion model derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in a natural coordinate system which follows the general direction of the channel flow. In the model studied, Eulerian-Lagrangian method is used to solve the stream tube dispersion equation. The stream tube dispersion equation is decoupled into two components by the operator-splitting approach; one is governing advection and the other is governing dispersion. The advection equation has been solved using the method of characteristics and the results are interpolated onto Eulerian grid on which the dispersion equation is solved by centered difference method. In solving the advection equation, cubic spline interpolating polynomials is used. In the present study, the results of the application of this model to a natural channel are compared with a steady-state flow measurements. Simulation results are in good accordance with measured data.