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- W4294795409 abstract "The paper deals with option pricing under the classical Black-Scholes model and a more sophisticated Merton jump– diffusion model, which allows jumps in the underlying asset price. The Merton model is represented by non–stationary integro– differential equations. Due to the integral term, standard methods are not very efficient because they lead to full discretization matrices. The Black–Scholes model can be considered a particular case of the Merton model, which does not contain the integral term. In the paper, a method is proposed, which is a combination of the Crank–Nicolson scheme and the wavelet–Galerkin method using adaptive quadratic spline wavelet basis selected a priori. This enables to significantly decrease the number of basis functions and size of matrices and vectors involved in computation compared to standard non–adaptive wavelet–Galerkin methods. Furthermore, the proposed wavelet–based method leads to sparse discretization matrices with uniformly bounded condition numbers." @default.
- W4294795409 created "2022-09-06" @default.
- W4294795409 creator A5044810274 @default.
- W4294795409 date "2022-01-01" @default.
- W4294795409 modified "2023-09-24" @default.
- W4294795409 title "A priori selected spline–wavelet basis for option pricing under Black–Scholes and Merton model" @default.
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- W4294795409 doi "https://doi.org/10.1063/5.0100641" @default.
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