30 % of the time the put is going to finish ITM. No disagreement on that point. The calls are always OTM when that 30 % occurs. Of the other 70%, part of the time the calls will finish OTM and part of the time, the calls finish ITM. The question is how often the calls finish ITM. The answer is 30% of that 70%, or 21% Thus one of the options finishes ITM 51% of the time. 60% is not the correct answer. Here's another way to look at it: The calls finish OTM 70%. The puts finish OTM 70% The chances that BOTH of those things will occur is .70 * .70, or 49% of the time. Thus, 49% OTM and 51% ITM. Sync - please let me know if this makes sense to you. It is the correct answer. Mark http://blog.mdwoptions.com/options_for_rookies/
Please note that a basic property of probability theory is that the probability of occurrence of either of two mutually exclusive events is the sum of their respective probabilities. If A,B mutually exclusive then P(A+B) = P(A) + P(B) In the general case P(A+B) = P(A) + P(B) â P(AB) If event A is : call ITM and event B is : put ITM , the two events are mutually exclusive (if A occurs then B cannot occur and vice versa). So P(A+B) = 0.3 + 0.3 About your calculations I would like to point out that P(AB) = P(A)P(B) only if A and B are independent events. For example, âThe calls finish OTM 70%â, âThe puts finish OTM 70%â are not two independent events so multiplying their probabilities will not give a correct answer.
Mark, Last week I read a similar example that you posted on your blog. I did not understand it then and I still don't understand it now. I figured out how to do this in TOS and it indicates around 40% OTM.
My intuition tells me the answer is 51% You have a 70% chance squared of NOT reaching those strikes .7 x .7 = .49 Therefore the inverse has to be 51%.
Look, only one of three outcomes is possible in a strangle: 1) The price of the underlying is above the higher strike at expiration 2) The price of the underlying is below the lower strike at expiration 3) The price of the underlying is between both strikes at expiration There is a 30% chance that either 1 or 2 will occur, and a 40% chance of 3 occuring. Both 1 and 2 cannot occur at the same time. However, until expiration, the path that the price takes could very well move it below the lower strike and then all the back up above the higher strike. The probabilites only predict what will happen at the time of expiry. For an IC, the math is the same to figure the probabilities between the long and short leg.
The underlying will touch your short strikes very often. What is important is what you do when that happens. Panic by closing the IC? Close the losing spread? Close the winning spread? Add another IC? Do nothing? Once the IC is placed, it is all about management; the odds of events occuring really mean nothing--especially since the greeks are dynamic, not static.