Is there any mathematical basis to this gut feeling?
The only "mathematical" basis would be one whereby IV sold was higher than the real volatility (HV) turned out to be. Legging in / out sucessfully may be a contributing factor to that feeling - but that's nothing to do with options - that's your personal skill.
it implies that the volatility is such that there is a low probability of the stock moving more than 50 in either direction
Almost, but not quite. Remember that the basis of option pricing is fair value, i.e. where over the long run you will neither gain nor lose money. So the implication in your example is that half the time the underlying will move up 100 points, and half the time the underlying will move down 100 points (the direction is of equal chance, but the magnitude is determined by the implied volatility).
ATM Put sold for 50...
Up 100 points - you profit 50 (the premium)
Dn 100 points - you lose 50 (100 - the premium)
Expected outcome - Zero
The same applies to a straddle (sold for 100), where half the time the underlying will rise 100 points (you make / lose zero) and half the time it will fall 100 points (you make / lose zero). Again, expected outcome - zero.
Therefore the seller has a statistical edge. On the other hand the buyer is not in profit until the stock moves more than 100
Yes, but the seller is not in profit unless the stock moves less than 100. Both scenarios are dependant on the volatility of the underlying.
My second glass of red has just slid down, so hope that makes sense.
Happy new year to all.... and hope it's a mega lucrative one at that :-)
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