Random? "Not all the time"... is correct.
Sure, and instead of thinking to replace one unfair coin with another one during tosses it makes a million times more sense to start with a much better function that better describes asset price moves than a binomial or coin toss. That was actually my point. Coin tosses and binomial distributions make students understand the discrete math behind derivatives pricing but continuous pricing is an entirely different animal.
Coin tosses and binomial distributions make students understand the discrete math behind derivatives pricing but continuous pricing is an entirely different animal.
The binomial model converges to the same result with far more parsimony than any continuous ito calculus derived solution. More importantly the binomial model is computationally tractable and doesn't rely on the discretization of an SPDE which is subject to some error as a result of the translation from continuous to discrete space.
Only a rube would prefer complicated and obscure to simple and straightforward. But whatever makes you feel smarter, I guess.
OK, excellent answer. But what if every flip is an unfair toss. Market is 50/51 but 20,000,000/1,000. Still a flip at 50/51, but definitely not fair, and certainly not fair between 49 and 52.
Modeling it makes no difference, I don't trust those things much anyway. Just something I've been pondering lately.
Really? I traded and structured exotic rates derivatives at several sell side banks for years. How come continuous stochastic models were used throughout, such as the SABR model? Has nothing to do with smarter. You talked out of your ass without knowing at all what market practitioners use. Even for vanilla derivatives or barriers, binomial model are hardly ever used. Your claim that binomial models are used for pricing is flat out wrong.
Dude, I like some of your content but hell, when you get riled up about certain social issues that someone may disagree with you (as in another thread) , you get all fired up and aim bazookas at the messenger. Not that I care, I have a very thick skin. But it would help to stay factual in this thread. Fact is that market practitioners use other discretizations than the binomial model.
The people answering "does not matter" are true degenerates. Only a degenerate gambler would bet without knowing where the odds lie.
it is about market being random or not and this clearly shows that market is not random and money can be made, if you are willing to wait for these patterns.