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Article

Černá, Dana
Wavelet method for option pricing under the two-asset Merton jump-diffusion model. (English). In: Chleboun, J., Kůs, P., Přikryl, P., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 21-26, 2020. Institute of Mathematics CAS, Prague, 2021. pp. 30-39
MSC: 47G20, 60G51, 65M60, 65T60 | DOI: 10.21136/panm.2020.03
Keywords:
Merton model; wavelet-Galerkin method; integro-differential equation; spline wavelets; Crank-Nicolson scheme; sparse matrix; option pricing
Summary:
This paper examines the pricing of two-asset European options under the Merton model represented by a nonstationary integro-differential equation with two state variables. For its numerical solution, the wavelet-Galerkin method combined with the Crank-Nicolson scheme is used. A drawback of most classical methods is the full structure of discretization matrices. In comparison, the wavelet method enables the approximation of discretization matrices with sparse matrices. Sparsity is essential for the efficient application of iterative methods in solving the resulting systems and the efficient computation of the matrices arising from the discretization of integral terms. To illustrate the efficiency of the method, we provide the results of numerical experiments concerning a European option on the maximum of two assets.
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