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 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 Rotisserie Spike 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 Rosin Core Solder interval and applied as a single block matrix equation for the valuation of options on a 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.