Firstly, I do not have a quant finance background. This is new to me, and I imagine that this is a basic question for this group.
I am calculating the price of a binary/digital option with closed-form equations derived from a Black-Scholes analysis. More specifically, I am using the Black-Scholes valuation for a Cash-or-nothing call.
The option period that I have been asked to calculate ends every hour, on the hour. I am sampling the underlying every 5 seconds. How should I scale and/or calculate my volatility if I want to use the 'normal' approach (but assuming a 0 mean). These are all annualised to one year. Should I still do the same?
More specifically, I am curious how I scale the standard deviation of the sum of the square log returns in this case?