Estimating daily volatility of unevenly/irregularly spaced time series data

Say I have time-series data that is unevenly spaced, with anything between 4-50 hours of spacing in between. The data comes from a trading account history, which has captured the balance of the portfolio after each trade.

I'd like to calculate the annualised daily volatility of this account in order to compute a sensible Sharpe ratio. As such, I am assuming volatility does not vary with time.

I've read How do you estimate the volatility of a sample when points are irregularly spaced? but do not have access to the knowledge, experience or computational power required to solve for the maximum in the formula proposed.

What would be a reasonably good way to approximate the daily volatility of this time series? I can think of a few solutions and would be interested to hear if you have comments on them or if you had other ideas.

• Solution #1: Pretend my data is, in fact, regularly spaced
• Solution #2: Cut all but the last data point of each day
• Solution #3: As #2 but fill any gaps with some short EMA estimate (perhaps making use of Eckner, 2015)
• Solution #4: Use a method akin to that oulined in pp.38 of Eckner, 2014, (if I've understood it correctly) and approximating the vol to the ATR scaled by $$\sqrt{ \frac{ \pi }{ 8 \rho } }$$
• The realized variance $v=\sum_i (x_{i+1}-x_i)^2$ generalizes to $v=\sum_i (\frac{x_{i+1}-x_i}{t_{i+1}-t_i})^2$ when the time intervals are unequal, but deterministic. (Assuming a zero mean for simplicity). – Alex C Oct 27 '18 at 21:43
• @AlexC Indeed my intervals are deterministic as I am looking at historical returns. If I've understood you correctly: assuming zero mean (happy to do this, as this is already the convention I would use to calculate volatility normally), I can simply scale each return by the inverse of the time taken to realise that return, and then calculate the standard deviation (as per usual) on these scaled returns? – Doggie52 Oct 28 '18 at 21:41
• Yes. But let's first see if someone upvotes my comment... – Alex C Oct 28 '18 at 22:53