Option pricing: A yet simpler approach

Abstract

We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox-Ross-Rubinstein (CRR) pricing model. The main tool used in the paper for cleaning up the reasoning is applying static hedging arguments. This can be accomplished by taking various routes through some auxiliary considerations, namely Arrow-Debreu securities, digital options or backward random processes. In the last case the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end we discuss the paradox involving the drift parameter $\mu$ in the BSM model pricing. We provide sensitivity analysis and the speed of converge for the asymptotically vanishing drift.