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Hello Stuart and others,
Some comments - sending to the list to invite response from other option
traders:
>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.
1. If sigma = "std deviation", I would think that 4 deviations is like a
0.002% chance of occurence?
In any distro, the event is recorded only upon occurence - after the fact.
a. Even if a 4 sigma event happens, the probability of 2 consecutive 4-sigma
events happening back to back is practically non-existent?
b. One would still need to watch this "tail" and probably be better off not
trading the option market in a tail event unless one is
- extensively capitalized,
- has an accurate directional or volatility bias,
- and guts of steel
c. If one does have an accurate directional assessment and still wants to
trade a tail event, trading the underlying has a better risk/reward
profile - because at these tail events, especially in the major indices and
equities,
either
- the rules of the game get changed (increased margin, lesser supply,
lack of liquidity at desired prices, fast market conditions upsetting your
balance)
or
- the premium erodes faster than directional bias benefit.
Case in point: Oct 28, 1997 - SnP, Intel, IBM options v/s underlyings.
>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
Yes, works ONLY if reversal takes place at the 2 sigma levels. However,
there are many times when 2, even 3 consecutive 2-sigma moves happen in the
same direction, chewing up your trade - because it has a directional bias.
This is where delta-neutral trading (or volatility trading) becomes
relevant - you're playing volatility expansion/contraction, not direction.
>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.
I experience the following:
If IVol is significantly below HVol, prices are glued around its mean, and a
half-sigma event is in progress. Since even a half-sigma event is not normal
behavior, prices should move back to a one or 2 sigma level. Direction is
difficult to predict using only volty readings, one needs technical analysis
to work this out. However, this is where volatility expansion is definite
because volatility is mean reverting - whichever volty you're looking at -
IVol, HVol. Thus a volatility trade is good since a small move in the
underlying will cause a disproportionately large move in the option premium.
If IVol is significantly above HVol, prices are already recording a 2-3
sigma event. As explained above, a directional bias is useless if trading
options, because a greater percentage move in the underlying is needed to
double the price of the option. Again, a volatility capture trade is
profitable, if the circumstances allow.
If Ivol is anywhere between these 2 zones, directional spreads work or even
naked bullish or bearish positions work. Volatility capture is difficult -
or pointless - coz at the market maker's side, whichever model is being used
to compute option price/volty (Monte Carlo/B-S/Coxx etc), the market maker's
spread between expected returns and the t-bill/dividend yield spread are
narrow - so they are neutral to direction already, and by consequence option
holders tend to benefit or lose almost proportionately with the underlying's
performance.
This is why the general "trusim" probably emerges - trade only at-the-money
or in-the-money options - coz these have delta of 0.5 or better, which
dampens your portfolio's volatility.
Regards
Gitanshu
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