None of the pricing models are scientifically absolutely accurate. For continuous pricing the log normality distributional assumption is not accurate but has very nice mathematical properties for random variable transformations and change of risk measures.
Random does not imply a lack of predictability. There is an underlying distribution from which all values in the universe of movement are pulled from. The reason there are major pullbacks after huge movements is because the probability of that movement occuring was low, and the following movement will most likely be near the center of the distribution (where you would expect any value to be).
Probability is a difficult field to understand. Random processes don't necessarily imply un-forecastable processes. To think that shows a fundamental misunderstanding of the mathematics of probability.
The people answering "does not matter" are true degenerates. Only a degenerate gambler would bet without knowing where the odds lie.
If I throw a ball 10 times into a basket does that mean on the 11th time it will make it in - or is it some function of probability - the environment (market noise), my mentality (strategy), and my team (market sentiment)?
Your comment regarding pullbacks after large moves is not accurate for statically distributed price returns. A large move one direction will not result in large moves the other way (if this is what you mean by pullback). Such behavior is indicative of autocorrelation in returns which forces us to leave the binomial pricing model you mentioned in later comments.
Does this look random ?
The log return series is stationary, which implies reversion to the mean in extreme moves. While it's a "stylized" fact take the log return of any index and you will find reversion to it's mean. In fact, I have no evidence for this but it seems like stationarity is necessary and sufficient for calling a series mean reverting.
A pullback to the mean is not indicative of autocorrelation it is a property of a random variable undergoing an extreme move. Are you claiming that if I run a study where I measure the height of people in America, and I measure 3 people who are 7 feet tall, that the next person being 5 foot 9 inches indicates there is autocorrelation in that series? That's preposterous. Any random variable will behave this way whether or not it's autocorrelated.
The binomial option pricing model operates under the same assumptions as the black scholes model. I am not even sure what you are talking about. Whereas @GRULSTMRNN had a point that the SABR model is probably what professional market makers use - you are actually fundamentally wrong. The reason you leave the BSM/Binomial model universe is to allow volatility to vary not some autocorrelation.