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A couple of Options Traders have weighed in with the same answer. WayneL of sigmaoptions talks about frequency or what is commonly referred to as probability, combined with the dollar amount that is won or lost.

Never a truer word said. Probability of win is irrelevant on its own.

The expectancy equation has two parts, 1) probability of win and 2) win size vs loss size. One way of expressing this mathematically is with this equation:

Expectancy = ((1 + reward/risk ratio) * win/loss ratio)-1

Dean also confirmed the same thinking I have basically the same answer, save for a couple of further thoughts.

Probabilities, or frequencies that are calculated via Black-Scholes, Binominal Tree or even the more esoteric methodology of GARCH, all essentially utilise a Gaussian distribution of stock prices in their volatility calculations.

This as the old saw notes, generally works well, until it doesn’t. Mandelbrot created a new mathematics to deal with this [and other problems] which while obviously genius, doesn’t as yet offer much practical help in calculating probabilities.

Thus, calculations of probability via the previously mentioned models use the lognormal distribution of the historical data. The future is however what we are interested in. With lognormal distribution data, 2 Standard deviations captures some 98% of the data.

Fat tails describe the data that falls outside of this 2 Standard deviations, and when selling Options, these are the data points that can basically destroy your trading account.

An 8 Standard deviation move has a probability of 0.000000000000000629 In other words, this should only crop up once in the life of the universe. You could, on this basis, bet the Bank, [as the Bankers have done] and sell Options, of course the premium you would receive for being this far out of the money would be pennies and in addition, you might have to add a time component to the deal to allow it to exceed brokerage costs.

Of course, what that tends to do is the following: it brings the sellers of premium in closer, talking in a Standard Deviation manner, to the ATM Strikes, say, 3 Standard Deviations, although, more likely to the 2 Standard deviation envelope.

Now the sellers are exposed. Just what really happens in the market? Let’s look at some historical examples from 1999

Ticker………………….%Change……………..STD
ASDV…………………….[-14.4%]………….-31.2
ANT………………………[-12%]……………-11.2
AMTD…………………….29.13………………..8.6
CHKP……………………[-10.8%]……………-8.4
TSG………………………8.5%………………..8.0

Taking a low VIX day: July 25 1993, on that day 12 stocks had, or exceeded 4 Standard Deviations, major stocks, US Steel, Bethlehem Steel, Chiquita Brands being amongst the stocks involved.

Last September and October in 2008, we saw volatility jump to unprecedented levels, moves in excess of 2 Standard Deviations happened daily, for weeks at a time.

In summary, selling premium, exposes you to the possibility of really large losses from two sources: the first is the movement of stock prices that significantly exceed their historical probabilities expressed in lognormal distributions, the second being the jump in Implied Volatilities as quoted by the market makers.

Last year especially, the spreads opened up to 50%+ on the bid/ask on pretty much any Option you care to name. This pretty much always happens during a high market volatility period. The result is that even if you think that you can roll out of the trade, the spreads will pretty much kill that proposition for you. You of course might not have any choice in the matter – however this is basically a Martingale system and requires extremely deep pockets, notice however that it again is predicated on a lognormal distribution.

Margin calculations on naked selling are nasty. Margin calculations on a losing position, requiring the ability to roll – are nastier still. I was involved funnily enough in a real time discussion about this very question, viz. selling premium is a high probability event based on the fact [alleged] that 90% of Options expire worthless. It became quite an acrimonius discussion, however, he [the seller] was caught in a 6 STD move and was wiped out. This was not some BioTech stock, rather it was the FTSE index.

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So circa $180K to hold a small loss of about $300 [original figures are in Pounds Sterling] For a retail trader, this is just insanity. The figures come from the previous discussion that I mentioned, once the market started to move against the position.

In summary, selling premium is very risky. I’m not saying don’t do it, simply that you cannot via any of the current models calculate the probabilities of the trade. What you can calculate however is the risk/reward ratio if you assume bad market conditions. That is ugly.

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