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Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment

Rafael Company;  Lucas Jódar;  Enrique Ponsoda — 2008

Banach Center Publications

This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time t d . Firstly the shifted delta generalized function δ ( t - t d ) appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent of the...

Approximations and error bounds for computing the inverse mapping

Lucas Jódar;  Enrique Ponsoda;  G. Rodríguez Sánchez — 1997

Applications of Mathematics

In this paper we propose a procedure to construct approximations of the inverse of a class of 𝒞 m differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.

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