Professor Wolfinger,

Please correct me if I’m wrong but you never mention the use of a probability calculator (e.g., Monte Carlo Probability Calculator) as a way to get help in choosing the strike prices and hence, a position with a good risk/reward profile for a spread or iron condor (IC).

Is it useless or is delta good enough for checking the probability or is there some other reason

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Minyan Dimitris
 

You’re right. I’ve never discussed using a probability calculator, and it's time to correct that oversight.

Those calculators are far from useless.

In addition to the calculator mentioned above, Peter Hoadley offers another. But unless you buy his software package, use of the free online version is limited.

What does a probability calculator do?

It calculates the probability for the occurrence of specific events.

This discussion is about the probability calculator and the useful information it can provide. Thus, I'm going to talk about expiration and the chances that an option will finish (expiration closing price) in the money (ITM) or out of the money (OTM). If you’re like me, and prefer not to own positions through expiration, you can change the number of trading days to agree with how long you intend to own the position.

Another important point: In this discussion, ITM simply means in the money. Clearly it makes a difference whether the option is $0.10 or $10 ITM. Thus, just because the option is ITM at expiration, it doesn’t mean you have a loss. It depends how far ITM. This idea isn’t part of today's post.

Probability of option expiring worthless

As a premium seller, it's important to know the chances that the option you sold will be in the money when expiration arrives. You must decide whether the potential reward justifies the risk -- and the probabilities can be considered when making that decision.
Option buyers also benefit by having a good idea of how often their option will finish in the money. As with premium sellers, when the option is held through expiration day, all-time premium is lost and the profitability of the trade is determined by how far ITM the option moves.

What you already know

Option traders already know the chances an option will finish ITM because the option delta gives a good approximation of that probability.

But that's not enough information to evaluate the risk of owning a specific position. More information would be useful -- unless you’re someone who opens the trade, closes their eyes, and opens them on expiration Friday. That's too risky for me, but some iron condor traders do just that. If that describes your modus operandi, then the probability of expiring worthless is all you have to consider when looking at probabilities.

For everyone else, there’s more to consider. These probability calculators provide very useful information, including the probability that one or both options will be in the money -- at some time -- before the options expire.

Probability of underlying reaching a specific price

You can calculate the probability that the underlying stock or index will move far enough before expiration arrives, so that it touches a specific price. For most traders, the strike price is the number used.

But there are alternatives. For example, a trader who depends on technical analysis may want to determine the probability of hitting a resistance or support price.