An alternative approach to solving the Black-Scholes equation with time-varying parameters

Authors

Marianito R. Rodrigo, Instituto Tecnológico Autónomo de MéxicoFollow
Rogemar S. Mamon, Brunel University

RIS ID

86646

Publication Details

Rodrigo, M. R. & Mamon, R. S. (2006). An alternative approach to solving the Black-Scholes equation with time-varying parameters. Applied Mathematics Letters, 19 (4), 398-402.

Abstract

In this note we provide a simple derivation of an explicit formula for the price of an option on a dividend-paying equity when the parameters in the Black-Scholes partial differential equation (PDE) are time dependent. With the aid of general transformations, the option value is expressed as a product of the Black-Scholes price for an option on a non-dividend-paying equity with constant parameters, the ratio of the strike price in the time-varying case to the strike price in the constant-parameter case, and a modified discount factor containing a parametrised time variable.