Estimating Historical Volatility from Irregularly Spaced Prices

Summary

The document asks how to estimate annualized historical volatility when price observations arrive at unequal time intervals. Its baseline method for evenly spaced data calculates returns over a fixed window, takes their sample standard deviation, and scales for the sampling interval. The proposed alternative for irregular samples sums squared price changes divided by their respective time intervals, divides that total by the full observation window, and takes the square root to obtain volatility.

This gives a concise realized-variance-style estimator that avoids resampling the prices. The answer does not provide a derivation, empirical comparison, or guidance on implementation details such as the time units, return transformations, market closures, or microstructure noise. Its formula should therefore be understood as a suggested calculation rather than a fully validated procedure for every sampling scheme or asset. The document also leaves the precise definition of the observation window and annualization convention to the user.

Key ideas

• For evenly spaced observations, the described baseline scales return dispersion by the sampling interval.
• For irregular samples, the proposed estimator weights each squared price change by its elapsed time.
• The accumulated variance measure is divided by the full window before taking its square root.
• The answer provides no derivation or empirical validation and leaves time conventions unspecified.

Tags

# Historical volatility from non-uniform samples


# Historical volatility from non-uniform samples












The way I compute historical volatility is that I take two parameters $dt$ and $T$, get a list of stock prices with the step of $dt$ over the window $T$ (so $T/dt+1$ samples in total), compute $T/dt$ returns from this prices, compute their sample standard deviation, and scale using $\sqrt{dt}$ to annualize it.

In case I have non-uniformly sampled data, i.e. $dt_1\neq dt_2 \neq \dots$ I wondered whether I can compute annualized historical volatility without resampling?

## Answer by nbbo2 (score 1)

https://quant.stackexchange.com/a/22931

What I would do :

Step 1. Calculate $V=\sum_i \frac{\Delta P_i^2}{dt_i}$

Step 2. Annualize V. $V_a=\frac{V}{T}$

Step 3. Find $\sigma = \sqrt{V_a}$

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