A Review of the Generalized Black-Scholes Formula & It’s Application to Different Underlying Assets

Abstract

The Black-Scholes (1973) formula is well used for pricing vanilla European options. There are several different variations used by market practitioners dependent on the underlying asset being modelled. In this brief paper we present the generalized Black-Scholes representation, outline it’s derivation and review how to configure the model appropriately for different asset classes. In particular varying the cost of carry term incorporated in the model allows us to express the generalized Black-Scholes as the classical Black-Scholes (1973) formula or the canonical Black (1976) representation.

Keywords: Generalized Black-Scholes, Derivation, Black Model, Cost of Carry, European Option Pricing, Put-Call Parity, Put-Call Super-Symmetry

JEL Classification: A30, A31, A33, C02, C20, C50,C60, C65, G15