So maybe youve heard of so called "fat tails" and you've definitely heard of black scholes normal distributions, gaussian cupolas and whatnot and whatever quant stuff under the sun which is going down. turns out most of that is total bollaks. but the good is that these things may provide trading oportunities which are profitable its basically trading on herd behaviour...
Imagine the stock market as a series of discreet 1 day games and not as a continuous time series as most people do... at any one time there are people long and people short and people that might be short or might be long in future... the thing is as price moves against one of these groups they become poorer and it is perfectly possible even over a 1 day horizon that these people may become how do they say it "stopped out" .... this is kind of similar to the reflexivity you may read in such books as alchemy of finance by Soros...
btw there is no such thing as a "Black Scholes normal distribution" - only a Black Scholes option pricing model, with asset returns based on a normal distribution.
w.r.t to continuous time - unless you can show in an alternative method and simpler way to solve the PDE's to obtain the Black Scholes solution using a discrete time step - it is the way to go. People are aware of this unrealistic assumption and duly account for it in their risk measures e.g. up-down delta etc
Yes, I already stated the model is based on a normal distribution, but is not a distribution in itself, which you have suggested.
Bollocks? It's a mathematical model - robust and using Occam's razor - assumptions such as continuous time, log-normal are actively adjusted for practicality e.g. in vol and tenor skews, term structure, Greek measures [up-down delta, vol bucketing etc]
EU only? More like the whole world
Leptokurtosis is also possible from random data - it doesn't always mean there's a trend present.
All the measure means is kurtosis, > 3 [normal]
It sounds like you're working on time convergence...
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