Alziary, Bénédicte and Takáč, Peter (2012) Option Pricing for Stocks with Dividends: An Analytic Approach by PDEs. Monografıas de la Real Academia de Ciencias de Zaragoza (n° 38). pp. 125-136.

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Abstract

We study the Black-Scholes equations for pricing options on stocks by splitting it into two simpler PDEs that can be solved by analytically simpler and numerically faster methods than the original Black-Scholes PDE. We first use a deflator process to arrive at a numeraire S(interest-neutral stock price) computed from the first equation and then obtain a simple Black-Scholes equation for the interest-neutral call option price P with no explicit dependence on the (instantaneous short) interest rate r. We also formulate two theorems on the solvability of these PDEs.