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First correction.
Sheldon Natenburg" Beyond the question of exact
distribution..the normal distribution has one serious flaw..its symmetrical"
p61Option Volatility and Pricing
Secondly Black Scholes uses normally
distributed BUT its a continuous time model and assumes volatility is
constant over the life i.e continuously compounded. The effect of these two
assumptions is that possible prices are LOGNORMALLY distributed. Thisis
how they intoduce leptokurtosis (fat tails).
Stocks DO NOT random walk. In many areas it has
been observed that correlations between observations far apart in time decay to
zero slower than expected of independent data or classic Markov type
models. Hurst (a British hydological engineer) was the first to note the
persistence of Nile flood data. Wet/dry years in the past affected
future flows. This is a memory event. After Mandelbrot , self similarand
related stationary processes with long memory were introduced to statistics.
Closer to home...if there was no memory in the market and it was truly random
walk how do support and resistance zones develop? Because people have
memory. The reason for academics and economists to use random walk isthat
it makes the math more tractable and subject to providing neat analytical
answers. From purely personal observation I believe economists are the
worst traders. They might be right in the end but a trader can get wiped
out in between.
If techniques are to be used such as Gann
with implicit assumptions it is important to understand them. Remember
Long Term Capital Management. Mr Scholes plus three other nobel
economics winners were involved when it went belly up with $ billions
lost. If any body should have known the assumptions they should. But
I presume their arrogance in curve fitting and random walk got beaten up because
its not. A second (maybe even the main factor) it failed because no MM was
employed. A proper assessment of risk was not employed.
As far as any Amibroker users reading all
this are concerned I hope they begin to feel that seeking a perfect
indicator is not on. That it's a constant evolution and a need to stay
flexible with their ideas and adapt. And also that a twenty line
price manipulation or logic string pales compared to the grunt thrown at
the markets by hedge funds. Nevertheless such things still work and work
well over long periods. I'm convinced that
its sticking to a rigorous trading strategy, planned before you start, clear
what you expect to happen when you get in and when/how you are getting
out. Its not 80% winners on every trade that are being looked for its80%
gains on those that do live up to the trend expectation. And if hit rate
is only 1 in 5 so long as less than 8% was lost each loser you'll be
ahead.
Just my thoughts. I hope it cleared up some
of yours.
P
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The square property you try and ascribe to normal
distribution of prices is incorrect, prices are probably log normal.
They also have long memory (hurst et al). So its at best an
approximation - which is OK so long as its borne in mind while using
it.
The Black-Scholes model of
option pricing is based on a normal (random walk) distribution of price
movements. Random walk (Brownian motion) models result
in an expected price excursion that varies with the square root of
time. Over time, stock price movement have been shown to randomly
distributed, so the fact that the square root factor pops up in both theory
and practice is not surprising. So to directly address your comment,
prices are probably not log normal distributed. I have not read the
MIT studies for sometime, but I believe that was their conclusion
also.
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