macrocephalopod

6/ Remember, BS assumes vol is constant in time. Every timeslice is the same as every other. So if we want to calc sensible vols, we need to calc a sensible clock for the stock. A way to “divide time” so that the clock ticks off constant chunks of volatility. In theory at least.

7/ This is impossible to do perfectly. If you knew what vol was going to be in the future, just trade it! What we’re really after is a decent approximation. So here’s a thing we can do:

8/ A. Take 5min returns of the stock intraday (or whenever options trade) and overnights/weekends. B. Calculate variances for every block for a few years. C. Aggregate by days in the monthly exp cycle. This variance-time is now our measuring stick.

9/ Lots of variance on a Monday morning from 9:35am to 9:40am? Time flows fast in that 5min block. Of course we should probably renormalize variances so that the units are still roughly days or years or something intelligible. Hopefully you get the idea.

10/ Yes there are problems with this approach. Q: What if the stock had earnings on some day? A: Probably we need to throw that out for our var-time calculation.

11/ What else? Q: Does it make sense to have a different var-time for different stocks? A: Technically probably yes, but they should be fairly similar to each other in the same country, or size, or sector or whatever. Probably some aggregation is in order.

12/ More questions: Q: How far back should we sample data for? A: Bias vs variance tradeoff. Again. Q: What about if you had a market crash in your dataset? A: I dunno, maybe throw it out? Depends.

13/ Yet more: Q: Why aggregate monthly? Why not weekly? A: Weekly could be sensible...