Alternative methods to derive the Black-Scholes-Merton equation

Abstract

We investigate the derivation of option pricing involving several assets following the Geometric Brownian Motion (GBM). First, we propose some derivations based on the basic ideas of the assets. Next, we consider the trivial case where we have n assets. Finally, we consider different drifts, volatilities and Wiener processes but now from n stochastic assets taking into account a fixed-income.