Volatility and BlackScholes

motivated by a discussion on the Wealthy Boomer
Okay, so we need to determine some Volatility value so we can stick into the
BlackScholes formula.
In Excel, that'd be:
BS = S*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T)/(V*SQRT(T)))  K*EXP(Rf*T)*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T)/(V*SQRT(T))V*SQRT(T))
where
S = Stock Price
K = Strike Price
Rf = Riskfree Rate
V = Volatility
T = Time (in years) to expiry
Should we use the Standard Deviation of annual returns over the past umpteen years
or maybe the Standard Deviation of monthly returns
(multiplied by SQRT(12) to get an "annualized" number)
or maybe the Standard Deviation of daily returns (annualized !)
and then there's the question of which magic formula should one use to calculate Standard Deviation and ...
>Huh?
The way to calculate Standard Deviation or Volatility varies from one guru to another. For example:
 To determine a stock's historical volatility, calculate the equilibrium level (midpoint) of a stock's price range. Then simply divide the difference between the high point and the equilibrium level by the equilibrium level to get the volatility percentage.
 Volatility is found by calculating the annualized standard deviation SD of daily change in price
 where ??? is either N or N1
 or maybe where P_{t} is the stock price at time t
 or maybe ...
>So?
Presumably, for BlackScholes, one wants a Volatility number which gives a good estimate of the actual
value at which the option is currently trading. That is ...
>Pick the definition that best fits the current option premium, right?
Sure. Why not?
Or one can ignore the definitions and just fiddle with the Volatility number until you get a good BlackScholes value.
>And you'll use that to bid on an option?
No. I'm not interested in options.
I'm interested in what Volatility value will give a BlackScholes value which agrees with the current option premium.
For example, I look at GE call options and the current GE stock price and I fiddle with the Riskfree rate and
Volatility value and get the charts here
First I notice that changing Rf, the Riskfree Rate, isn't as important as picking a good V
.. that's the Volatility.
>The Riskfree might be 2% to 6% ...
Yes, and the Volatility can vary quite a bit:


>And, to make a long story short ...?
Uh ... yes. There's a spreadsheet.
It looks like this:
Click on the picture to get the spreadsheet
... and play with the numbers
>And did you play ... to find the best value for Volatility?
Yes, and I found that using the Standard Deviation of monthly returns for the past year
(multiplied by SQRT(12) to get an "annualized" number)
gave a good result. I also used SD, from #3 above, with ??? = N.
>And that's the correct choice?
Define "correct".
