The adaptive mesh model: a new approach to efficient option pricing

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

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Design, implementation and validation of advanced lattice techniques for pricing EAKO — European American Knock-Out option

International Journal of Financial Engineering ◽

10.1142/s2424786319500324 ◽

2019 ◽

Vol 06 (04) ◽

pp. 1950032 ◽

Cited By ~ 1

Author(s):

Mattia Fabbri ◽

Pier Giuseppe Giribone

Keyword(s):

Numerical Methods ◽

Adaptive Mesh ◽

European American ◽

Knock Out ◽

Lattice Methods ◽

Mesh Model ◽

Real Market

The paper presents a series of advanced lattice methods aimed at evaluating an EAKO European-American Knock-Out contract. The first part of the paper deals with the numerical methods implemented for pricing: Binomial and Trinomial Stochastic trees, Adaptive Mesh Model, Pentanomial and Heptanomial lattice. In the second part, specific tests are designed to validate the code written in Matlab language. The study concludes by applying the most performing model to a real market case.

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Conditional entropy maximization for PET image reconstruction using adaptive mesh model

Computerized Medical Imaging and Graphics ◽

10.1016/j.compmedimag.2007.01.001 ◽

2007 ◽

Vol 31 (3) ◽

pp. 166-177 ◽

Cited By ~ 5

Author(s):

Hongqing Zhu ◽

Huazhong Shu ◽

Jian Zhou ◽

Xiubin Dai ◽

Limin Luo

Keyword(s):

Image Reconstruction ◽

Conditional Entropy ◽

Adaptive Mesh ◽

Entropy Maximization ◽

Mesh Model ◽

Pet Image Reconstruction

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Pricing Discrete Barrier Options with an Adaptive Mesh Model

The Journal of Derivatives ◽

10.3905/jod.1999.319127 ◽

1999 ◽

Vol 6 (4) ◽

pp. 33-43 ◽

Cited By ~ 35

Author(s):

Dong-Hyun Ahn ◽

Stephen Figlewski ◽

Bin Gao

Keyword(s):

Adaptive Mesh ◽

Barrier Options ◽

Mesh Model

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MAGO: A NEW APPROACH FOR ORTHOPHOTOS PRODUCTION BASED ON ADAPTIVE MESH RECONSTRUCTION

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-2-w11-533-2019 ◽

2019 ◽

Vol XLII-2/W11 ◽

pp. 533-538

Author(s):

S. Gagliolo ◽

B. Federici ◽

I. Ferrando ◽

D. Sguerso

Keyword(s):

Iterative Process ◽

Point Cloud ◽

Input Data ◽

Adaptive Mesh ◽

Test Case ◽

New Approach ◽

Surface Models ◽

Best Fitting ◽

Mesh Reconstruction ◽

Orientation Parameters

<p><strong>Abstract.</strong> Orthophotos are one of the most common and typical products of a photogrammetric post-processing and, since the diffusion of specific software, their generation and usage have become even more widespread. In spite of it, some issues remain on the accuracy of orthophoto reconstruction, which is often downgraded by the introduction of meshes and Digital Surface Models to be used as surfaces representing the object. The use of a more accurate and reliable input, such as a point cloud, makes these approximations avoidable. For this reason, a new approach, termed MAGO (Adaptive Mesh for Orthophoto Reconstruction), is here delineated and proposed. The input data of the procedure are the user-defined orthophoto plane, the image and its internal and external orientation parameters, and a point cloud representing the object. Each pixel of the image is projected on the orthophoto plane at its original resolution via an iterative process, which builds an adaptive mesh, defined by means of the three best fitting points, where the collinearity rays and the point cloud intersect. After an overview on the method and its innovative features, an example on a test case is reported, together with a comparison between MAGO’s and another photogrammetric software results.</p>

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A new multiscale air quality transport model (Fluidity, 4.1.9) using fully unstructured anisotropic adaptive mesh technology

Geoscientific Model Development Discussions ◽

10.5194/gmdd-8-4337-2015 ◽

2015 ◽

Vol 8 (6) ◽

pp. 4337-4374

Author(s):

J. Zheng ◽

J. Zhu ◽

Z. Wang ◽

F. Fang ◽

C. C. Pain ◽

...

Keyword(s):

Air Quality ◽

Transport Model ◽

Control Volume ◽

Transport Phenomena ◽

Adaptive Mesh ◽

Mesh Model ◽

Adaptive Resolution ◽

Flow Features ◽

Mesh Resolution ◽

Mesh Technique

Abstract. A new anisotropic hr-adaptive mesh technique has been applied to modelling of multiscale transport phenomena, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been setup for two-dimensional (2-D) transport phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes.

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