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# Using a Probability Calculator

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## In addition to delta, these tools can enhance your risk/reward position.

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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

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.

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.

Let's look at an example:

RUT is 514.92

RVX is 29.34, and we'll use that as the volatility

As of Monday morning, November expiration is six weeks or 39 days (30 trading days) in the future. The Hoadley calculator uses calendar days and the Monte Carlo calculator uses trading days.

Assume we trade the following iron condor, collecting a premium of \$1.60.

NOTE: This is an example, not a recommendation, so please don't ask why I chose this IC. [It's based on the premium available, and yes, I know it's far from delta neutral]

252 trading days in one year

Sell RUT Nov 530/540 put spread

Sell RUT Nov 670/680 call spread

Delta of 540 put: 11.6; delta of 670 call: 16.8; total delta: 28.4

A. Using the Monte Carlo Probability Calculator (MCPC), 10,000 trials is maximum allowed.

Results: 10,000 is not that many trials. If you run this several times, you will get different results each time.

1. Delta says there's a 28.4% chance that one option will close ITM and MCPC says 29.48

2. The calls will move ITM one-third of the time; the puts move ITM one time in six. There's a greater than 50% chance that one of the options will move ITM. If you're someone who manages risk carefully, that suggests you'll be making an adjustment most of the time. And that's even more true if you adjust in stages and don't wait until one of the options has moved into the money.

If the idea of knowing you'll be forced to make an adjustment so often bothers you, then you have little choice but to sell call and put spreads that are farther OTM. Or, you can trade a stock or index that's less volatile. Either way, that means smaller premiums.

3. The probability that each of the short options will be in the money is near zero. But, if you find yourself making an adjustment on one-half of the position, I believe it pays to exit the winning side of the iron condor when it reaches a satisfactory low price.

1. Probability that one will end ITM: 27%. This is lower than the other calculator or delta predicted.

2. This calculator shows a higher probability of either option moving into the money: 36% vs. 33% for the calls and 18.4% vs. 17.4% for the puts.

3. There's low probability of both being ITM at one time or another, but again, the probability is a bit higher using this calculator.

Probability calculators provide information "that can be of significant value when used in a conscientiously applied program of option trading and regular risk management."

No positions in stocks mentioned.

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