Abstract
In this paper we investigate two efficient numerical methods for solving the Black–Scholes equation for pricing European options. We use spectral methods to discretize the associated partial differential equation with respect to space (asset direction) and generate a system of ordinary differential equations in time. This system is then solved by applying the numerical inversion of the Laplace transform which is based on the Talbot’s method [A. Talbot, The accurate numerical inversion of Laplace transforms, IMA J. Appl. Math. 23(1), 97–120 (1979)]. This involves an application of trapezoidal rule to approximate a Bromwich integral. Using Cauchy’s integral theorem, we deform the Bromwich line into a contour which starts and ends in the left half plane. Comparative numerical results obtained by this and other three methods (Exponential Time Differencing Runge–Kutta Methods of order 4, MATLAB solver ode15s and Crank-Nicholson’s method) are presented.
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Acknowledgments
E. Ngounda acknowledges the Agence National des Bourses du Gabon for the financial support. Patidar’s research was supported by the South African National Research Foundation.
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Ngounda, E., Patidar, K.C. (2015). A Laplace Transform Approach for Pricing European Options. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_37
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DOI: https://doi.org/10.1007/978-81-322-2485-3_37
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