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- W2965074413 abstract "This contribution deals with the numerical solution of the Black-Scholes equation. The Crank-Nicolson scheme is applied for time discretization and wavelets are applied for space discretization. Hermite cubic spline wavelets with four vanishing moments are adaptively used because they enable higher order approximations, are well-conditioned, have short supports, have a high potential in adaptive methods due to the four vanishing wavelet moments and mainly because arising stiffness matrices are sparse in wavelet coordinates. Due to irregularities of the initial data in the Black-Scholes model, the use of the second-order Crank-Nicolson scheme usually requires a certain amount of damping to compensate for the known weak stability of this scheme. We numerically show here that optimal convergence rate for a proposed adaptive wavelet discretization in space can be obtained without any damping and without any restriction on the time step. A numerical example is given for the Black-Scholes equation with real data from the Frankfurt Stock Exchange. We also compare numerical results for adaptive and non-adaptive wavelet discretization in space." @default.
- W2965074413 created "2019-08-13" @default.
- W2965074413 creator A5088754155 @default.
- W2965074413 date "2018-08-01" @default.
- W2965074413 modified "2023-10-18" @default.
- W2965074413 title "Adaptive Wavelet Based Scheme for Option Pricing" @default.
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- W2965074413 doi "https://doi.org/10.1109/mcsi.2018.00034" @default.
- W2965074413 hasPublicationYear "2018" @default.
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