# How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model.

Originally I thought the path dependency exists because in binomial tree model, we will price the options in a back-propagating fashion. We evaluate the price at time T, and then go backwards to calculate the price at time T-1. The dependency is from $P_{T - 1}$ to $P_{T}$. When I went over the Monte Carol Simulation approach to price options, I found that in Monte Carol Model, the price of option at time T depends on that at time T-1. The difference is that this dependency is from $P_T$ to $P_{T-1}$. However, per my understanding, we cannot say Monte Carol Simulation is a path dependent algorithm.

So how could I understand/explain the path dependency in binomial tree model when pricing options?

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If you are keen on this question, you can try to express the $\sigma$-algebra filtration with respect to which the price process $V$ of a derivative has to be measurable in order to be priced correctly by a tree model. (In the case of a Monte-Carlo simulation, this filtration is the filtration associated to the Brownian motion driving the simulation, so that there is no real limitation.)