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

100%

Company R., Jódar L., Ponsoda E.

Banach Center Publications

2008

tom 83

nr 1

37-47

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 considered sequence of the nice type. Illustrative examples including the comparison with the exact solution recently given in [2] for the case of constant yield discrete dividend payment are presented.

Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems

100%

Navarro E., Company R., Jódar L.

Applicationes Mathematicae

1993-1995

tom 22

nr 1

11-23

In this paper we consider Bessel equations of the type $t^2 X^{(2)}(t) + t X^{(1)}(t) + (t^2 I - A^2)X(t) = 0$, where A is an n$\times$n complex matrix and X(t) is an n$\times$m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Banach Center Publications

2 Company R.

2 Jódar L.

1 Navarro E.

1 Ponsoda E.

1 2008

1 1993

Wyniki wyszukiwania

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

Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems