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June 14th, 2012, 12:12 AM   #1
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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
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June 14th, 2012, 10:10 AM   #2
fam
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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)
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June 14th, 2012, 11:06 AM   #3
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Re: Stock Option probability question

Thanks.. got it..

But I cant calculate the 1.15.. hows that worked out ?
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June 14th, 2012, 01:14 PM   #4
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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
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June 14th, 2012, 01:29 PM   #5
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Re: Stock Option probability question

Thanks
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