Quadratic Variation to estimate Volatility

[quotes]

since dSdS=σσSSdt

Isnt't more straight forward to add up (St+1-St)^2 to estimate the volatility for a Geometric Brownian Motion?

 

[quotes]

Shreve uses (log(St+1)-Log(St))^2 to estimate the volatility.

 

[koupparis]

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.