Rose, Could you tell me how to obtain the Standard Deviation (the sigma of the normal distribution) from implied volatility data? I would expect the SD to be expressed in dollars .. so that, for example, the mu (the mean) might be $60 and the sigma $20.
optionsanalysis.com
lists iv=64%, for example. Sixty-four percent of what? The stock price? The exercise price? Of Unity? This has me stumped. How does one obtain the SD from this value?
The reason I'm asking is I developed an equation for the Profit Expectation, at least at expiration, of a buy stock-write call strategy .. had to break out my old statistics and calculus books .. cough .. cough. The eq'n requires SD as an input variable.
As to the eq'n obtained .. intuition tells me that with options being a zero sum game .. that my Profit expectation should be zero .. random walk and market efficiencies, etc. But for the Expectation to be zero, standard deviation would need to be about $75 for a $60 stock (AOL) .. an SD which seems too high.
This brings me full circle .. to cross-check by finding SD another way.
Your feedback will be appreciated. If you know of another thread for which this topic would be more appropriate, please let know that too. Thanks.
Ron
P.S. For the curious, the eq'n .. unproven and untested .. obtained for the simple case of stock_price = call_strike_price is
E=M-(SD/(2*((2*pi)^1/2))where M is the premium received for the call. Of course, the equation assumes zero trading costs. |
