Stabilized Adams type method with a block extension for the valuation of options

Stabilized Adams type method with a block extension for the valuation of options

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We construct a continuous stabilized Adams type method (CSAM) that is defined for all values of the independent variable rawlings fungo on the range of interest.This continuous scheme has the ability to provide a continuous solution between all the grid points with a uniform accuracy comparable to that obtained at the grid points.Hence, discrete schemes which are recovered from the CSAM as by-products are combined to form a stabilized block Adams type method (SBAM).The SBAM is then extended on the entire interval and applied as a single block matrix equation for the valuation of options on a 5318008 non-dividend-paying stock by solving a system resulting from the semi-discretization of the Black-Scholes model.The stability of the SBAM is discussed and the convergence of the block extension of the SBAM is given.

A numerical example is given to show the accuracy of the method.