# Wydawnictwa / Banach Center Publications / Wszystkie tomy

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

### Tom 83 / 2008

Banach Center Publications 83 (2008), 37-47 MSC: 03H10, 91B24, 35K15. DOI: 10.4064/bc83-0-3

#### Streszczenie

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 $\delta(t-t_{d})$ 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.

#### Autorzy

• Rafael CompanyInstituto de Matemática Multidisciplinar, Edificio 8G
Camino de Vera s//n
46022 Valencia, Spain
e-mail
• Lucas JódarInstituto de Matemática Multidisciplinar, Edificio 8G
Camino de Vera s//n
46022 Valencia, Spain
e-mail
• Enrique PonsodaInstituto de Matemática Multidisciplinar, Edificio 8G