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Quadratic Variation to estimate Volatility

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6/11/10
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since dSdS=σσSSdt

Isnt't more straight forward to add up (St+1-St)^2 to estimate the volatility for a Geometric Brownian Motion?
 
The first will estimate the variance of S(t), which is not the usual sigma used in option pricing etc. The second method is what one uses to estimate sigma.
 

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