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Bob & RTers:
Allelujah! Praise the Lord! There's someone else out there who thinks like me!
I agree with you entirely. In fact I posted a message a couple of weeks ago which had a pretty interesting theory in it regarding the difference between a gaussian assumption of market activity and a fractal assumption. Basically I posed the question as follows:
* The Black Scholes equation assumes that market movement conforms to some sort of Brownian motion and therefore, under "normal" conditions (read IV = HV) option prices reflect probabilities of occurance that are normally distributed
* Edgar Peters has demonstrated that the "normal" assumption overestimates the market's movement at certain sigma levels and underestimates its movement at other sigma levels. This demonstration was based on about 90 years worth of Dow data.
* Therefore, does it stand to reason that the following option strategy is destined to work in the long run:
- buy options at the sigma level where the Black Scholes model typically underestimates the market's propensity to move to.
- sell options at the sigma level that the Black Scholes model typically overestimates the market's propensity to move to
Just to be clear, this hypothesis refers to sigma levels that are calculated using Historical Volatility (not Implied Volatility).
The logic being that in the long run, the market will underprice the former and overprice the latter.
Moreover does this strategy become more effective when, in the former case, IV is less than HV? And in the latter case when IV is greater than HV?
I have been eager to backtest the hypothesis and am perfectly willing to report my findings back to the group. But alas, I cannot locate historical option data.
At the risk of upsetting some of the group who think we shouldn't listen to anyone else (why, then, are they in the group?) I would WELCOME COMMENTS.
- Stuart
>>> <RJones2279@xxxxxxx> 07/22 2:12 PM >>>
Hi Stuart,
Thanks for the message. In a way my doubts relate to the fact that the SD is
related to a normal distribution of outcomes but if you look at the picture
historically in a number of markets the distribution is somewhat skewed. The
normal distribution says that the probability of a large event occurring is
only 0.5% within 3SD's of the mean. The only problem is that if you look at a
number of markets they display a definite "fat tailed" rather than normal
distribution over a very long time period. I understand that markets which
display these characteristics include:DJIA; yen/dollar; US TBonds.
Given this scenario the probability of a large event occurring outside 3SD's
is not 0.5% but maybe several percentage points (2-3%). What I am saying here
is what common sense observation tells us: the assumptions on which linear
statistics are based are just that- assumptions and the probablity of getting
caught out is in fact far higher than it appears from a simple reading of the
product of linear statistical analysis.
These "anomalies" have been rationalised as part of a long memory which some
have tried to explain via chaos theory (which I dont think they have done and
which I dont understand anyway).
My point here is that the real risks of some standard strategies are in fact
somewhat higher than people may think, but being a novice , I will stand to be
corrected on this.
Thanks
Bob Jones
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