Numerical solution of modified Black–Scholes equation pricing stock options with discrete dividend

A Radial Point Interpolation Method for Pricing Options on a Dividend Paying Asset

“…They studied the problem of maximizing the expected gain process over stopping times taking values in the union of disjoint, real compact sets. Company et al [3] obtained the numerical solution of a modified Black-Scholes equation modelling the valuation of stock options with discrete dividend payments. They used a delta-defining sequence of the involved generalized Dirac delta function and applied an approach based on the Mellin transforms.…”

A fast Fourier transform method for Mellin-type option pricing

“…Thereafter it was implemented in [34,33], where the authors provide solutions for European, American, and basket options on n = 2 underlying assets. For European options, weak payoff functions [9], discrete dividends [8], transaction costs [30], and the Black-Scholes matrix equation [10] have since been considered in detail. However, in all of these cases continuous dividends are omitted.…”

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

“…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.…”

“…where D δ (S) S is the dividend yield and δ(t − t d ) is the shifted Dirac delta function (see [7, p. 140]). Recently, an explicit solution of (1) with a discrete dividend yield, independent of S, and a general payoff function V (S, T ) = f (S), has been given (see [2]).…”

“…In this case the discrete dividend payment has got a constant dividend yield A. The solution of (44)-(45) is given by (see [2])…”