# How to calculate probabilty using options



## Seneca60BC (22 October 2008)

Hi All

I understand that one uses the normal distribution and the standard deviation to work out where a stock price will be in x number of days given y volatility.  However, how do you go about calculating the probability of this stock price closing at a particular price?

Cheers!


----------



## Grinder (22 October 2008)

Give hoadleys a try, would post the link but can't seem to retrieve it.


----------



## sails (22 October 2008)

Seneca60BC said:


> Hi All
> 
> I understand that one uses the normal distribution and the standard deviation to work out where a stock price will be in x number of days given y volatility.  However, how do you go about calculating the probability of this stock price closing at a particular price?
> 
> Cheers!




Hi Senaca,

Do you mean where the stock might close at expiry or where it might close on a given day?  Not really my area - WayneL is good on these type of mathematical probability questions - perhaps someone else can chime in here.

Anyway, if it is for expiry, I understand that the general rule of thumb is to use the delta of an option.  For example, an option with a delta of .3 has a 30% chance of expiring in the money.   However, the deltas keep moving with the stock, so not sure of it's usefulness.

The other thing is that sometimes large clusters of open interest at a particular strike can attract the stock to that strike price near or on expiry day.  Sometimes this works like magic and other times it fails miserably.  It's called the "maximum pain" theory  - it's supposedly where the most retail option traders will lose money.  

It's interesting to watch the large blue chips which have reasonable option volume on expiry day as so many of them do expire very close to a strike price - not necessarily with the most OI, but nevertheless it happens regularly.  It's known as "pinning to the strike" - would be great to know which strike the will attract the stock at expiry - would be a permanent ATM machine!   Might be worth doing a google search on both these theories.

Cheers


----------



## Seneca60BC (22 October 2008)

Hi Sails

Yes what I meant was calculating the probabilty of a Stock closing at a particular price say 30 days from today given HV calculated by the normal distribution and standard deviation.

For example,

Just say I have a Call Option on ANZ and by Break Even Point is $21.50 and currently the price is at $19.00, given volatility of 50%, what is the probability that the Stock price will hit $21.50 in 30 days.

Cheers!

PS Grinder, yea i know about that tool - but was wanting to work it out manually


----------



## mazzatelli1000 (22 October 2008)

sails said:


> Anyway, if it is for expiry, I understand that the general rule of thumb is to use the delta of an option.  For example, an option with a delta of .3 has a 30% chance of expiring in the money.   However, the deltas keep moving with the stock, so not sure of it's usefulness.




I have seen many discussions and the formulas for calculating probability of expiry and the formula for the delta of an option is similar but not mathematically the same. 
But those option traders in Chicago like to keep it simple and use delta instead as a ready rule of thumb.

Shouldnt matter too much for us retail traders


----------



## sails (22 October 2008)

Seneca60BC said:


> Just say I have a Call Option on ANZ and by Break Even Point is $21.50 and currently the price is at $19.00, given volatility of 50%, what is the probability that the Stock price will hit $21.50 in 30 days.




Sorry, it's out of my area - I prefer to leave the mathematics to experts like Peter Hoadley    He has a "probability cone" function that is available with the premium version.  I understand you want the formula - perhaps someone else can help you...


----------



## Grinder (23 October 2008)

Tried working out the formula Seneca, brain started to hurt as Im no mathamatician. As a retail trader I'll stick to Hoadleys prob analysis.

LoL


----------

