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. © 2005 Elsevier Ltd. All rights reserved.
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. https://doi.org/10.1016/j.aml.2005.06.012