SOLUTION OF BLACK-SCHOLES EQUATION FOR STANDARD POWER EUROPEAN OPTIONS WITH DISCRETE DIVIDEND PAYMENT

Abstract

The Nobel Prize celebrated option pricing formulas derived by Fischer Black and Myron Scholes for plain vanilla payoffs known as Black-Scholes formulas. They developed these formulas for pricing European call and put options based on certain assumptions in order to minimize risk factor. The underlying asset pays a constant dividend payment during the life of option was one of the assumption to derive these formulas. S. P. Zhu and X. J. He tried and succeed to improve this assumption by taking discrete dividend payments for underlying asset at fixed dividend date. They derived approximate Black-Scholes formulas of European options for plain vanilla payoffs. Note that standard power payoffs are the generalization of plain vanilla payoffs. This paper contributes to the derivation of approximate Black-Scholes formulas for standard power payoffs. Further, the accuracy of these formulas have been checked numerically.