or patternAug 24, 2019 · Definition of random (Entry 2 of 3) 1a : lacking a definite plan, purpose, or pattern.
if an pattern exists that is not random.
that means market is not random....
that the pattern means something or not is irrelevant
or patternAug 24, 2019 · Definition of random (Entry 2 of 3) 1a : lacking a definite plan, purpose, or pattern.
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.
since height is determined by GOD only He can answer that question.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?
Mean reversion commonly refers to an increased likelihood of positive (or negative) observations following moves in the opposing directions (like an OU process).

Absolutely not. Financial non interest rate asset time series are not stationary, they do not imply reversion to the mean in extreme moves. Through differencing though, for example, you can transform a random/stochastic process into a stationary process. Indexes never revert back to any mean because of any log return properties or for any other mathematical reason. No random process found in non-interest rate financial time series or distributions that define financial time series well have mean reverting properties that are dictated by mathematical principles. Interest rates do. Not others.
Hello padutrader,