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

• Volume: 83, Issue: 1, page 37-47
• ISSN: 0137-6934

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## Abstract

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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 $\delta \left(t-{t}_{d}\right)$ 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.

## How to cite

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Rafael Company, Lucas Jódar, and Enrique Ponsoda. "Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment." Banach Center Publications 83.1 (2008): 37-47. <http://eudml.org/doc/282447>.

@article{RafaelCompany2008,
abstract = {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.},
author = {Rafael Company, Lucas Jódar, Enrique Ponsoda},
journal = {Banach Center Publications},
keywords = {Black–Scholes equation; discrete dividends; variable yield; numerical solution; semidiscretization},
language = {eng},
number = {1},
pages = {37-47},
title = {Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment},
url = {http://eudml.org/doc/282447},
volume = {83},
year = {2008},
}

TY - JOUR
AU - Rafael Company
AU - Lucas Jódar
AU - Enrique Ponsoda
TI - Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment
JO - Banach Center Publications
PY - 2008
VL - 83
IS - 1
SP - 37
EP - 47
AB - 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.
LA - eng
KW - Black–Scholes equation; discrete dividends; variable yield; numerical solution; semidiscretization
UR - http://eudml.org/doc/282447
ER -

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