# Puzzle: Meaning of "sell a strike one SD above the current price"?



## jj1929 (5 March 2008)

From a book, I read the following strategy: sell a strike one SD above the current price.  Standard deviation was calculated using the implied volatility of the ATM option.
However, I don't understand what SD (standard deviation?) means.
I have a question: If the implied volatility of the at-the-money call is 25% with 17 days left before expiration and the current price of the undelying instrument is 133, what strike should I sell?


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## VolTracker (6 March 2008)

Standard deviation is calculated from volatility and time.

SD=V.sqrt(t)

If annualised volatility is 25% and time is 17 days (17/365 years) then...

SD= 0.25 * sqrt(17/365) = 0.054 or 5.4%.

If underlying is 133 then short strike would be 133*1.054 = 140 .


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## noident (17 March 2008)

VolTracker said:


> Standard deviation is calculated from volatility and time.
> 
> SD=V.sqrt(t)




Just wondering where this definition of the standard deviation came from?
I use the one described in http://en.wikipedia.org/wiki/Standard_deviation which is totally different. That's what I use in my calculations.
Also, strictly speaking standard deviation makes sense for a normally distributed set of values.


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## wayneL (17 March 2008)

Look up here: http://en.wikipedia.org/wiki/Volatility_(finance) for the correct calculation.

In finance (and particularly the options market,we are looking for the standard deviation of the instrument's logarithmic returns in the specified time period (sigma).

Generally the number of trading days is used.

Thus if you happen to have amibroker or metamumbojumbo, the formula for annualized volatility as calculated by the last 20 trading days of movement is:

(StDev(log(C/Ref(C,-1)),20)*sqrt(256))*100

Therefore, you can calculate sigma for the remaining trading days in the life of an option (say 17 trading days):

(StDev(log(C/Ref(C,-1)),20)*sqrt(17))*100

Cheers


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## chops_a_must (17 March 2008)

wayneL said:


> Look up here: http://en.wikipedia.org/wiki/Volatility_(finance) for the correct calculation.
> 
> In finance (and particularly the options market,we are looking for the standard deviation of the instrument's logarithmic returns in the specified time period (sigma).
> 
> ...




Thank you so much for that.

I was going to have spend days working out how to code the standard deviations and things.

If you have any other codings for options I would absolutely love them.


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## wayneL (17 March 2008)

No worries Chops

Bear in mind it is a precentage calculation.

Obviously the actual dollar amount can be obtained with a slight mod:

(StDev(log(C/Ref(C,-1)),20)*sqrt(17))*close

Here's a little adjustable one you can input the number of trading days left (in amibroker):

x = Param("Days Left",20,1,100,1);
y = (StDev(log(C/Ref(C,-1)),20)*sqrt(17))*C;
Plot(y,"Deviant Indicator",colorred,styleline);


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## wayneL (17 March 2008)

wayneL said:


> No worries Chops
> 
> Bear in mind it is a precentage calculation.
> 
> ...



Sorry, there is a mistake in the formula;

x = Param("Days Left",20,1,100,1);
y = (StDev(log(C/Ref(C,-1)),20)*sqrt(x))*C;
Plot(y,"Deviant Indicator",colorred,styleline);


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## wayneL (17 March 2008)

jj1929 said:


> From a book, I read the following strategy: sell a strike one SD above the current price.  Standard deviation was calculated using the implied volatility of the ATM option.
> However, I don't understand what SD (standard deviation?) means.
> I have a question: If the implied volatility of the at-the-money call is 25% with 17 days left before expiration and the current price of the undelying instrument is 133, what strike should I sell?



Just want to add a couple more comments here.

1/ My formula obviously refers to historical volatiltiy. The OPs question referred to implied volatility. This is where VolTracker's calc comes in. Both can (and should) be referred to when determining short strikes.

Remember, you are inherently making a volatility projection when selling gamma (going short options) in that you are projecting that the short strike hopefully stays outside of the future realized volatility.

2/ This may be obvious too, but some care should be taken *where* you measure sigma from. We all observe the wave structure of share movement (whether formally or not) and my tip is to select short strikes at potential pivot points (not floor pivots), because you can easily get 1 sigma retracements that will threaten short strikes in a normal wave pattern

Not comfortable. In other words, a little bit of rudimentary technical analysis is a huge help IMO.


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## noident (18 March 2008)

There's some confusion here.
There is only one standard deviation, the one, the only, defined in statistical analysis.
Finance appears to use standard deviation (of logarithmic return) when calculating a measure of volatility. (I admit I didn't know it, I'm only starting in shares/stocks).
This does not change the definition of standard deviation in any way though.


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## wayneL (18 March 2008)

noident said:


> There's some confusion here.
> There is only one standard deviation, the one, the only, defined in statistical analysis.
> Finance appears to use standard deviation (of logarithmic return) when calculating a measure of volatility. (I admit I didn't know it, I'm only starting in shares/stocks).
> This does not change the definition of standard deviation in any way though.




There is no confusion. It is exactly as you say in the discussion. The reason the term "one standard deviation" is used with reference to the option volatiltiy, is simply to ensure no multiple or fraction of sigma (volatility to 1 standard dev) is used.

But also bear in mind that stock market returns are not normal, they are far more likely to be leptokurtic (The fat tails that smack traders in the face... or hand stunning windfall profits). 

This is the reason that away from the money options may be higher priced than atm options... the so called volatility smile.

Also note that the usage of one standard dev and volatility in the sense used in this thread is applicable to option pricing formulae (Black-Scholes etc) and not really applicable outside of option trading.

You can use the normal St dev of closing prices for that. e.g. Bollinger bands etc.


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