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Journal Of Mathematics And Modeling In Finance (27830578) 4(1)pp. 19-35
This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with respect to the asset price variable. By using some vector and matrix calculations, we reduce the PDE to a system of linear equations that can be solved at each time step for different asset prices. We perform an error analysis to show the convergence of our technique. We also provide some numerical examples to compare our technique with some existing methods and to demonstrate its efficiency and accuracy. © 2024, Allameh Tabataba'i University. All rights reserved.
Computational Methods For Differential Equations (23453982) 11(2)pp. 281-290
A numerical method based on the Haar wavelet is introduced in this study for solving the partial differential equation which arises in the pricing of European options. In the first place, and due to the change of variables, the related partial differential equation (PDE) converts into a forward time problem with a spatial domain ranging from 0 to 1. In the following, the Haar wavelet basis is used to approximate the highest derivative order in the equation concerning the spatial variable. Then the lower derivative orders are approximated using the Haar wavelet basis. Finally, by substituting the obtained approximations in the main PDE and doing some computations using the finite differences approach, the problem reduces to a system of linear equations that can be solved to get an approximate solution. The provided examples demonstrate the effectiveness and precision of the method. © 2023 University of Tabriz. All rights reserved.
Journal of Computational and Applied Mathematics (03770427) 328pp. 252-266
One of the most important subject in financial mathematics is the option pricing. The most famous result in this area is Black–Scholes formula for pricing European options. This paper is concerned with a method for solving a generalized Black–Scholes equation in a reproducing kernel Hilbert space. Subsequently, the convergence of the proposed method is studied under some hypotheses which provide the theoretical basis of the proposed method. Furthermore, the error estimates for obtained approximation in reproducing kernel Hilbert space are presented. Finally, a numerical example is considered to illustrate the computation efficiency and accuracy of the proposed method. © 2017 Elsevier B.V.
CMES - Computer Modeling in Engineering and Sciences (15261492) 109(3)pp. 247-262
In this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for single- and two-asset options are illustrated. Copyright © 2015 Tech Science Press.
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics (12237027) 76(1)pp. 51-58
In this paper, we consider an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. We use the continuous linear Legendre multi-wavelets on the interval [0, 1) to solve this equation. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Tavassoli kajani m., ,
Vahdati, S. ,
Abbas, Z. ,
Maleki, M. Journal Of Applied Mathematics (16870042) 2012
Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method. © 2012 M. Tavassoli Kajani et al.
Australian Journal of Basic and Applied Sciences (19918178) 4(9)pp. 4193-4199
In this paper,We use the continuous Legendre multi-wavelets on the interval [0, 1) to solve Fredholm integral equations of the second kind. To do so, we reduced the solution of Fredholm integral equation to the solution of algebraic equations. Illustrative examples are included to show the high accuracy of the estimation, and to demonstrate validity and applicability of the technique. © 2010, INSInet Publication.
Applied Mathematical Sciences (discontinued) (1312885X) 3(13-16)pp. 693-700
We use the continuous Legendre multi-wavelets on the interval [0,1) to solve the linear integro-differential equation. To do so, we reduced the problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Comparison has been done with two other methods and it shows that the accuracy of these results are higher than them.
Abbas, Z. ,
Vahdati, S. ,
Tavassoli kajani m., ,
Atan k.a., Applied Mathematics and Computation (18735649) 210(2)pp. 473-478
In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a, b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine-Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions. © 2009 Elsevier Inc. All rights reserved.
AIP Conference Proceedings (0094243X) 971pp. 105-111
In this paper we extend the 2-D directed graphical representation for DNA sequences. The main purpose is to making a directed graph corresponding to a DNA sequence which hasn't any complete coincidence of the edges. To prevent repetition of the edge e we define e→1 by using the outer product of two vectors and some mathematical concepts. Moreover, we have applied this method for some DNA sequences to show the advantage of this method over the some other methods. © 2008 American Institute of Physics.
