I've been working on a model for pricing options that does not rely on volatility as an input. (I know: I might as well try to design an airplane without wings.) Testing it out on real prices, I've found that it give vastly different answers for most options. But when the stock price is fairly close to the strike price and the expiration date is only a few months in the future, my estimate doesn't stray too far from the market quote. So as a general options pricing model, this one pretty much fails.
But today I realized that I really don't care. The vast majority of options are ones I don't really care to sell in the first place. For the most part, I want to sell options with strike prices near the price I would value a company. And options longer than a few months in duration are not interesting either since it would be hard to value the underlying shares. Further, I don't really plan on selling options that are less than 50 or 60¢ because commissions eat up too much of the premium. In essence, my model pins a value on the options I'd really like to sell and I don't care what it does to options I want nothing to do with.
Now I'm interested in selling a January $22.50 option on Oracle that currently trades for 50¢. It's pretty far out of the money, so my model does a rotten job of evaluating its price. It comes up with a negative price, which obviously won't work. On the other hand, my model values the $20 option at about $1.32 while the market says the option is worth $1.50. If I were interested in selling Oracle at $20, I'd take that price, which would amount to selling Oracle at $21.50 with a 67% probability.
As it turns out, if Oracle where trading at $22.50 today, I estimate that the $22.50 option would be worth about $1.24. Now there isn't much chance that Oracle will jump from $20.21 to $22.50 in one day, but it does exist. And if it did happen, I'd gladly sell an option on my Oracle shares for that price. It would be a pitch I'd know what to do with.
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