# Possible to convert between continuous & discrete volatility without underlying data?

Is there a way to convert between continuous and discrete volatility without the actual return data?

For example, calculating on 12 monthly returns:

{0.03, 0.91, 0.05, -0.17, -1.64, 0.79, -1.41, 0.69, 1.08, 0.42, 1.29, 1.66}


from Ito's Lemma, volatility is

$\sigma =\sqrt{\frac{(dS)^2}{S^2 dt}}$

σ = 0.0352148


whereas using standard deviation

$\sigma =\sqrt{\frac{m}{T-1}\sum _{t=1}^T (r[t]-R)^2}$

σ = 0.035048


The reason for asking is I have annualised standard deviation and wish to compute confidence bounds for b = -2, -1, 1, 2. However $\sigma$ here is the continuous log version:

$y_0 e^{\left(a-\frac{\sigma ^2}{2}\right) t+b \sigma \sqrt{t}}$