# Why does option pricing not depend on probabilities in a binomial tree style valuation

I am new into learning option pricing and read that option pricing using binomial valuation does not depend on probabilities (real or risk neutral).

Example:

A 1 period binomial tree with $u = 1/d = 1.07$ and $S_0$ = $100. If the up-move probability$u$is 0.99 or 0.01, I read that the call option prices is the same and is equal to$4.8. They assumed European style options.

What you say is false. In general, the price of an option does not depend on physical probabilities but does depend on risk neutral probabilities. In your case, in a one-period binomial tree model, the probability of going up is $q=\frac{(1+r)-d}{u-d}$ therefore the price of the option paying $C_u$ and $C_d$ is $$C=\frac{1}{1+r}\left(qC_u+(1-q)C_d\right)=\frac{1}{1+r}\left(\frac{(1+r)-d}{u-d}C_u+\frac{u-(1+r)}{u-d}C_d\right)$$ If you focus on the second part of the equation it looks like the price does not depend on probability, but as the first part shows it does indeed depend on risk-neutral probabilities!