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 this paper for simplifying the reasoning is applying static hedging arguments. In applying the static hedging principle, we consider Arrow–Debreu securities and 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 Black–Scholes–Merton model pricing. We provide sensitivity analysis and an approximation of the speed of convergence for the asymptotically vanishing effect of drift in prices.

我们对 Cox-Ross-Rubinstein (CRR) 定价模型中的路径依赖型和欧式衍生品的定价进行了精益的、非技术性的阐述。本文中用于简化推理的主要工具是应用静态对冲参数。在应用静态对冲原则时，我们考虑 Arrow-Debreu 证券和数字期权，或反向随机过程。在最后一种情况下，CRR 模型扩展到无限状态空间，这导致了经典 CRR 模型中不存在的有趣新现象。最后，我们讨论了Black–Scholes–Merton 模型定价中涉及漂移参数\(\mu \)的悖论。我们为价格漂移的渐近消失效应提供了敏感性分析和收敛速度的近似值。