# Option pricing: A yet simpler approach

## TL;DR

This paper simplifies the pricing of path-dependent and European derivatives within the CRR model using static hedging techniques, extending to an infinite state space and analyzing the impact of drift parameters.

## Contribution

It introduces a simplified, non-technical approach to derivative pricing in the CRR model, including extensions to infinite state spaces and sensitivity analysis of drift effects.

## Key findings

- Extension of CRR model to infinite state space reveals new phenomena.
- Static hedging simplifies derivative pricing reasoning.
- Analysis of drift parameter effects on option pricing.

## 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.