Silent Fears in the Hearts of Option Credit Spread Writers : Probabilities of worries, scares, and their bigger sister the probability of an option account blow up

One of the things that strikes fear in the heart of option credit spread writers is the thought that the underlying stock or index might touche or finish above their short strike. There is an even bigger fear which is the thought that the underlying stock finishes above their long strike, which means a maximum loss, and an account blowup if they did not read about this risk in the other posts in this blog--check it up because the devil is in the details in an option credit spread business.

What the probabilities  priced in the options of such events? Let us see how we can compute them.

Assume an  ABC stock (or underlying index)  trading at say 100 (S=100). We have a call option at strike 110 (K=110) which is priced at  $0.50.  We assume we know the delta (denoted D) of the call option at strike 110. Assume  D=0.40 for this example.

One may say that the probability P we are looking for is delta. This is the typical answer you may read about in forum, books, etc. But it is not correct. In fact the value of P is , bless than delta (although not by much by the distinction is important).

Here is how one can compute the probability that the stock would end above strike 110. The quantity ($0.50 + (110- 100)* 0.40)/110 is the difference (D-P). Therefore to get P, we subtract the latter quantity from D. In this case, it is equal to 0.041. This means that the probability of the stock ending above strike 110 is 40% MINUS 4.1%, which is roughly 35.9%. So the answer is not 40%,  but ( a lower number). 35.9%.

Let us ask you a second related question: what is the probability that the stock visits strike 110? (Note that we are asking for the probability that it touches 110, and not the probability that it ends about 110 at option expiration.) We will give the details in a next post.

Now go brag about your new acquired knowledge to friend, and strangers in forums. I give you the bragging rights. :-)

Oh! Before you go. Did you calculate the probability that the stock ends above the strike of the long option in your option credit spread?

Since you are reading down here, may mean you want to know the answer of the touch probability. It is a little bit more than the double of 35.9%.  In this case, you will get scared 72% of the time if you write the 110 call option. A bit more than half will be false alerts, but you do not know in advance which is an alert, and which is the real thing.