Displaying similar documents to “Wavelet method for option pricing under the two-asset Merton jump-diffusion model”

Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets

Černá, Dana

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This paper addresses the two-asset Merton model for option pricing represented by non-stationary integro-differential equations with two state variables. The drawback of most classical methods for solving these types of equations is that the matrices arising from discretization are full and ill-conditioned. In this paper, we first transform the equation using logarithmic prices, drift removal, and localization. Then, we apply the Galerkin method with a recently proposed orthogonal cubic...

Approximate multiplication in adaptive wavelet methods

Dana Černá, Václav Finěk (2013)

Open Mathematics

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Cohen, Dahmen and DeVore designed in [Adaptive wavelet methods for elliptic operator equations: convergence rates, Math. Comp., 2001, 70(233), 27–75] and [Adaptive wavelet methods II¶beyond the elliptic case, Found. Comput. Math., 2002, 2(3), 203–245] a general concept for solving operator equations. Its essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l 2-problem, finding the convergent iteration process for the l 2-problem...

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

Wavelets and prediction in time series

Mošová, Vratislava

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Wavelets (see [2, 3, 4]) are a recent mathematical tool that is applied in signal processing, numerical mathematics and statistics. The wavelet transform allows to follow data in the frequency as well as time domain, to compute efficiently the wavelet coefficients using fast algorithm, to separate approximations from details. Due to these properties, the wavelet transform is suitable for analyzing and forecasting in time series. In this paper, Box-Jenkins models (see [1, 5]) combined...

Haar wavelet method for vibration analysis of nanobeams

M. Kirs, M. Mikola, A. Haavajõe, E. Õunapuu, B. Shvartsman, J. Majak (2016)

Waves, Wavelets and Fractals

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In the current study the Haar wavelet method is adopted for free vibration analysis of nanobeams. The size-dependent behavior of the nanobeams, occurring in nanostructures, is described by Eringen nonlocal elasticity model. The accuracy of the solution is explored. The obtained results are compared with ones computed by finite difference method. The numerical convergence rates determined are found to be in agreement with corresponding convergence theorems.