My Math Forum Stock Option probability question

 June 14th, 2012, 12:12 AM #1 Newbie   Joined: Jul 2010 Posts: 20 Thanks: 0 Stock Option probability question Ref: http://www.optionstradingsignals.com...ptions-part-1/ 1 Std Dev = 68% Probability 2 Std Dev = 95% Probability 3 Std Dev = 99% Probability This formula is fine for 1 Std Dev 1 Std Dev = Price x Volatility x SQRT( Calendar Days/ 365.25) 68% = Price x Volatility x SQRT( Calendar Days/ 365.25) ************* Question1: Whats the above formula for 2 Std Dev ? 95% = ??? Question2: Whats the above formula for any probability percentage ? 75% = ??? NOTE: I assume you dont change volatility to fit, as thats a fixed variable. Any ideas??? Thanks
June 14th, 2012, 10:10 AM   #2
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Re: Stock Option probability question

Quote:
 Originally Posted by icm63 Ref: http://www.optionstradingsignals.com...ptions-part-1/ 1 Std Dev = 68% Probability 2 Std Dev = 95% Probability 3 Std Dev = 99% Probability This formula is fine for 1 Std Dev 1 Std Dev = Price x Volatility x SQRT( Calendar Days/ 365.25) 68% = Price x Volatility x SQRT( Calendar Days/ 365.25) ************* Question1: Whats the above formula for 2 Std Dev ? 95% = ??? Question2: Whats the above formula for any probability percentage ? 75% = ??? NOTE: I assume you dont change volatility to fit, as thats a fixed variable. Any ideas??? Thanks
At first if we are talking about the Normal Distribution the relationship between the number of SD and % of the population in the interval is about:

2 Std Dev = 68% Probability
4 Std Dev = 95% Probability
6 Std Dev = 99% Probability

as you must consider both sides of the distribution mean.

Question1: Whats the above formula for 2 Std Dev ?
Lets say, 4 SD:
95% of the population (price) is in the interval = 4 x Price x Volatility x SQRT( Calendar Days/ 365.25) or 2 SD for each side of mean.

Question2: Whats the above formula for any probability percentage ?
First you must check the standard normal distribution for checking how many SD (each side of the mean) correspond to 75 %. If you do it, for 75% you will find 1.15 SD, then:
75% = 1.15 * 2 * Price x Volatility x SQRT( Calendar Days/ 365.25)

 June 14th, 2012, 11:06 AM #3 Newbie   Joined: Jul 2010 Posts: 20 Thanks: 0 Re: Stock Option probability question Thanks.. got it.. But I cant calculate the 1.15.. hows that worked out ?
 June 14th, 2012, 01:14 PM #4 Newbie   Joined: May 2012 Posts: 13 Thanks: 0 Re: Stock Option probability question You must use Standard Normal Distribution Table. You must know to read it, like that: At first you must divide the total probability 75 % by 2, because the Normal Distribution is symmetric. You get 37.5 % on each side of the mean; Second step is using the Table, looking for the probability value. On the present case near value of the table is 0.3749. Third and last step you must get the z value. You get it going from probability value (0.3749) horizontally (1.1) and vertically (0.05) and you will get z value like that: z = 1.1 + 0.05 = 1.15 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
 June 14th, 2012, 01:29 PM #5 Newbie   Joined: Jul 2010 Posts: 20 Thanks: 0 Re: Stock Option probability question Thanks

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