90% Probabilities and all that

["Stuart Hazlewood" <shazlewood@xxxxxxxxxx>]

The idea that an option position can provide a 90% chance of success is based on the Gaussian calculation of volatility (standard deviation), itself based on the assumption that market returns are distributed normally.

Edgar Peters' work on chaos theory suggests that this assumption  is fallacious.  Noteably, his analysis shows that a normal distribution  underestimates the occurrence of a +1 sigma event and a + or - 4 sigma event in the S&Ps.  It also overestimates the occurrence of a + or - 2 sigma event. (moreover, this holds true over any time frame - dailies, minute bars, whatever)

Which leads me to a bigger question:  Black Scholes is based on the assumption of a normal distribution.  If historical volatility equaled implied volatility, Black Scholes would be expected to predict the actual prices of options.  However, given the fractal nature of market returns, Black Scholes will underestimate the price at + 1 sigma and + and - 4 sigmas, and overestimate the price at + and - 2 sigmas.

Therefore, consistently applying the following spreads over a long enough period of time should prove profitable 

  long a call at 1 std dev above the underlying and short a call at 2
  std devs above the underlying

  long a put at 1 std dev above the underlying and short a put at 2 
  std devs below the underlying

Now of course the fly in the ointment is that implied volaility nearly always differs from historical volatility.  Which leads to the question:  does it increase the odds even higher to go long a 1 std dev above and short at 2 std devs above if ...

  implied volatlity is below historical at 1 std dev above

  implied volatility is above historical at 2 std devs above

  both of the above.

Thoughts, opinions, mockery or abuse will be willingly accepted.

  -  Stuart
  

>>> "David Rosenthal" <davidr@xxxxxxxxxx> 06/06 7:39 PM >>>
> One big difference between being patient in a Poker game and
> being patient in
> the Market is that in Poker your odds of wnning can surpass 90%
> (i.e. with a Straight Flush).  Whereas in the market your odds never reach
> that level. (If you have such a trade, call me, I'll pay for the call -
and your time.)

There are ways of trading short options where the odds of winning surpass
90%.  Unfortunately, unless you have a good risk control plan in place, one
loss can exceed 9 times the average win...

  David Rosenthal
  <davidr@xxxxxxxxxx>