Using a Probability Calculator when Trading Options


Please correct me if I am 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 IC.

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

Thank You



You are right.  I have 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.  Unless you buy his software package, use of the free online version is limited.


What does a probability calculator do?

Needless to say it calculates the probability for the occurrence of specific events. 

discussion is about the probability calculator and the useful
information it can provide.  Thus, I'm going to be talking about
expiration and the chances that an option will finish (expiration closing price) ITM or OTM. 
If you are 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.

important point: in this discussion ITM simply means in the money. 
Clearly it makes a difference whether the option is 10 cents or 10
dollars ITM.  Thus, just because the option is ITM at expiration, it
does not mean that you have a loss.  It depends how far ITM. This idea is
not 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 are someone who opens the trade, closes his/her 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 is 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 this morning, Monday 10/12/2009, November expiration is 6 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 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 is a greater than 50% chance that one of the options will move ITM.  If you are someone who manages risk carefully, that suggests you will 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 will 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 is 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.

b) Using the Hoadley calculator


1) Probability that one will end ITM: 27.0%.  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) 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."

Does anyone recognize the origin of most of the words in the final paragraph? It's not fair to use any search engine.


8 Responses to Using a Probability Calculator when Trading Options

  1. John Forman 10/12/2009 at 7:49 AM #

    The one thing I would toss out there is that a probability is only as good as the distribution upon which it is drawn. The basic Black-Scholes model, for example, is based on the use of the Normal Distribution, which has long been debunked as representing actual market reality (ask Taleb, et al). most notably, the odds of a large move happening are higher than the normal distribution would suggest. The bottom line is that you need to understand your tools and know their strengths and limitations.

  2. Mark Wolfinger 10/12/2009 at 8:02 AM #

    I completely agree and thanks for the clarification.
    These models provide a reasonable facimile of the information sought, but they do have their limitations. Depending on the data as something that’s completely reliable is a mistake. It’s a first approximation.
    It can help users understand that the odds of moving ITM during the lifetime of the position is much greater than the odds of finishing ITM, but the results are not exact – and the really big moves – the ones that result in the largest losses -are understated.

  3. Rob Shepherd 10/12/2009 at 9:19 AM #

    “that can be of significant value when used in a conscientiously applied program of option trading and regular risk management.”
    Good morning Mark,
    I’m going to take a wild guess: McMillan?
    The book is 1000 pages long, so I figure I have a fair chance of being correct.
    Thanks for the informative post! Regards, Rob

  4. Joe 10/12/2009 at 9:32 AM #

    “that can be of significant value when used in a conscientiously applied program of option trading and regular risk management.”
    hmm….that reminds me of a Listerine commercial…or was it Crest? “can be of significant value when used in a conscientiously applied program of oral hygiene and regular professional care”…or something like that.

  5. Mark Wolfinger 10/12/2009 at 9:38 AM #

    Hi Rob,
    You are the first guesser, and that’s not correct.
    This is probably not a fair qwuestion because it comes from a 1960s TV commercial. And many (most?) readers weren’t even botn then!

  6. Mark Wolfinger 10/12/2009 at 9:59 AM #

    Your quote is accurate. And it was Crest toothpase.
    Back when flourides were newly added to toothpaste and drinking water.
    Well done.

  7. Dimitris 10/12/2009 at 3:38 PM #

    Using your data from the example above (premium=1.60, probability it closes beyond either limit=29.48%) and assuming that no action is taken until the IC expires, I calculate the expected return of this trade as follows:
    Max loss = 1000-160=840. If I make this trade 1000 times, 295 (29.48%) times I will make a profit of $160 and 705 times I will have max loss of $840, ie a net loss of $545000.
    Using a probability calculator, no matter what strike prices I choose (very risky or very conservative or something in between) I always get a loss when I “trade” an IC and assume that I will not take any action until the IC expires.
    If this is right, then my conclusion is that the only way to make a profit trading IC’s (or credit spreads) is ALWAYS making adjustments at a certain stage before expiration.
    Is this correct?
    Thank You

  8. Mark Wolfinger 10/12/2009 at 5:17 PM #

    As detailed below, in general I agree, but quibble with your conclusion that the ONLY way…is to ALWAYS…
    1) Premise one is incorrect (705 max losses). You must determine how often the index finishes beyond the strike of the option you own because NOT ALL losses are maximum. Some are small and some ‘losses’ will be profits when the index is only slightly in the money.
    But this correction will not make up a half million dollar loss.
    2) You can improve your P/L figures over 1000 iron condor trades by using longer term options. Without making the calculations, you can see that if you choose an IC with about the same delta, you can collect a higher cash premium by using a longer term option. If you collect $300 instead of $160, your expectation is better than break even. [earn $300 about 700 times and the other 300 times your worst result will be to lose $700, but part of that time you lose less, or even earn a profit.
    So, it’s not as bleak as it appears to you.
    3) I would put it this way: If you NEVER make adjustments you can expect to lose money over an extended period of time – for the iron condodrs you chose to study.
    I would not say that one must ALWAYS make adjustments. Because sometimes the options fade into oblivion. Quietly.
    But your idea that adjustment are necessary – a sutsbattial part of the time is in agreement with my beliefs.
    Please recognize this is not a rigorous mathematecal analysis, and could be incorrect.
    Apparently adjusting is important. And that’s what my experience tells me.
    I suggest you consider adjusting in stages. Try a practice account. Or if you have the patience, try to find a simulator to look at many of the gazillion possibilities. don’t ignore getting whipsawed.
    Or better yet, begin by owning insurance and see how that works out for you.
    It’s difficult to know when to make the first adjustment, but you can pick a delta (for the short option) or the total delta for the position to make the first adjustment. But afyet that you have many choices of what to do.
    Play with the numbers.