Calculation of historical/realized volatility

[morganpbrown]

I see a variety of methods used to calculate historical and realized volatility. Is one or the other most "correct"? Also the calculations depend vigorously on window size. "Best" window size?

(Seems to me that a decaying weighted average - with max weight at "today" - would make most sense and reduce sensitivity to window size)

Big picture conceptual question - Are we assuming that historical volatility is a predictor of today's implied volatility? And likewise are we assuming that today's implied volatility is a predictor of future volatility?

Happy New Year to all of you and thanks in advance

 

[BlueWaterSailor]

I see a variety of methods used to calculate historical and realized volatility. Is one or the other most "correct"? Also the calculations depend vigorously on window size. "Best" window size?

(Seems to me that a decaying weighted average - with max weight at "today" - would make most sense and reduce sensitivity to window size)

Big picture conceptual question - Are we assuming that historical volatility is a predictor of today's implied volatility? And likewise are we assuming that today's implied volatility is a predictor of future volatility?

Happy New Year to all of you and thanks in advance

Happy New Year to you as well!

So: historical and realized are - well, facts. They done been, as a laconic friend of mine is likely to say. And while window size is theoretically variable, the usual meaning for historical, as far I'm aware (at least I haven't seen anyone use or make a case for anything different) is a year. Whether it's 252 or 365 depends on what you're doing with it - the latter is, of course, the span in which the former (trading days) is included - but the intent for them is to cover the same period.

Realized is - and again, I'm leaning into the only usages I know, which means I could be wildly wrong - applicable to a given trade. It's the vol that was realized at a given point during that trade. No window size would apply. Taken together, the set of RV values forms the path that vol takes during the trade.

And neither of them is a predictor of any sort (don't I wish... actually, no - because if it was, then nobody would pay me for the risk, so, nuh. Skip that train of thought.) IV is literally what it says; that is, a value that is implied by the combo of put/call, S, K, t, and r. It's a thing that we back out of all those via the BSM (or whatever other model we're using) - a "fiddle factor" if you happen to speak Engineering. The necessary tweak that we, the guys on the production floor, have to apply to make the idealized numbers that the eggheads up in the office hand us actually work. Sometimes, we have to file off a corner; sometimes we'll weld a little extra length onto the rebate flange; other times, just a bit more grease and some extra oomph on the 20-ton press will make it happen.

But IV has mean-reversion characteristics that price doesn't, so you can use it as part of your market perspective in order to figure out which way the frog might jump. (Don't lean on it too hard - it's not going to give you any guaranteed answers - but it definitely is a useful factor in figuring out a trade.)

 

[ajacobson]

realvol.com calculates for many of the benchmarks and it's free. CME listed some of them as tradeable, but too few to the party, and they were delisted. Box has the license now, but needs a tradeable future to make it work.

 

[morganpbrown]

Hi guys. funny you mention realvol.com; their page, which shows two formulae, was my initial source of confusion!

https://www.realvol.com/VolFormula.htm

Here's what I am trying to do. Below is plot of SPY price (red) and a ratio (yellow) of "IV" (average over all strikes & expirations on a given day) to "RV" (computed by realvol.com's formula 1 in a 30-day forward window).

For example, I would divide the IV on December 1 by the RV from December 1-30. If the ratio is >1, then the IV is overestimating the volatility that actually occured, and I should be selling options. And vice versa.

Obviously I can't use this ratio as a predictor, since I need to look 30 days into the future to compute it! It's kind of interesting, though, that the ratio seems to stay in either a depressed or elevated state for some period of time, before flipping to the other state. Makes you think that there's some predictability to how the ratio mean-reverts. Kind of suspicious, though, that the length of the troughs & peaks is about the same 30-day window size that I used to compute RV.

 

[Matt_ORATS]

Happy New Year to you as well!

So: historical and realized are - well, facts. They done been, as a laconic friend of mine is likely to say. And while window size is theoretically variable, the usual meaning for historical, as far I'm aware (at least I haven't seen anyone use or make a case for anything different) is a year. Whether it's 252 or 365 depends on what you're doing with it - the latter is, of course, the span in which the former (trading days) is included - but the intent for them is to cover the same period.

Realized is - and again, I'm leaning into the only usages I know, which means I could be wildly wrong - applicable to a given trade. It's the vol that was realized at a given point during that trade. No window size would apply. Taken together, the set of RV values forms the path that vol takes during the trade.

And neither of them is a predictor of any sort (don't I wish... actually, no - because if it was, then nobody would pay me for the risk, so, nuh. Skip that train of thought.) IV is literally what it says; that is, a value that is implied by the combo of put/call, S, K, t, and r. It's a thing that we back out of all those via the BSM (or whatever other model we're using) - a "fiddle factor" if you happen to speak Engineering. The necessary tweak that we, the guys on the production floor, have to apply to make the idealized numbers that the eggheads up in the office hand us actually work. Sometimes, we have to file off a corner; sometimes we'll weld a little extra length onto the rebate flange; other times, just a bit more grease and some extra oomph on the 20-ton press will make it happen.

But IV has mean-reversion characteristics that price doesn't, so you can use it as part of your market perspective in order to figure out which way the frog might jump. (Don't lean on it too hard - it's not going to give you any guaranteed answers - but it definitely is a useful factor in figuring out a trade.)

When I managed a group of floor traders, we had a method for calculating HV using tick data and simulating scalping gamma and converting the profit into a vol. This was time consuming and expensive but gave us an edge because our findings matched what we were experiencing in the market.
We found that the Parkinson method of calculating vols were the closest to our tick calculation and now at ORATS we present our modification of the Parkinson method orHV and we present close to close as well in our API.

 

[qlai]

we had a method for calculating HV using tick data and simulating scalping gamma and converting the profit into a vol.

Using tick data as apposed to the Close of the day? So you used some combination High/Low/Close?
Also, do you mind explaining what it means to simulate scalping gamma? You mean you used your calculations to better price options, so you were essentially Market Making? When you say "convert profits to vol" do you mean you used the profits to buy volatility/gamma? Sorry, but I'm sure I'm not the only one on this forum wandering this means

 

[morganpbrown]

Using tick data as apposed to the Close of the day? So you used some combination High/Low/Close?
Also, do you mind explaining what it means to simulate scalping gamma? You mean you used your calculations to better price options, so you were essentially Market Making? When you say "convert profits to vol" do you mean you used the profits to buy volatility/gamma? Sorry, but I'm sure I'm not the only one on this forum wandering this means

Here's a link explaining the Parkinson method (I haven't read it yet)

https://www.ivolatility.com/help/3....nson number, or High,on a fixed time interval.

 

[Matt_ORATS]

Using tick data as apposed to the Close of the day? So you used some combination High/Low/Close?
Also, do you mind explaining what it means to simulate scalping gamma? You mean you used your calculations to better price options, so you were essentially Market Making? When you say "convert profits to vol" do you mean you used the profits to buy volatility/gamma? Sorry, but I'm sure I'm not the only one on this forum wandering this means

Scalping gamma means delta neutral hedging the change in delta caused by gamma and a move in the stock. For example, we would give ourselves an imaginary 1000 gamma and follow delta neutral rules like flatten out deltas every .5 stdev move in the stock or every $1 move in the stock, and flatten out at the close. The simulated profit is calculated off of the change in the stock price and the average delta over that price move. For example, if you had 1000 gamma and the stock moved $1 you would make your average delta over the move of 500 (0 starting + 1000 ending / 2) * $1 = $500. We had a way of converting that $500 back into an implied statistical historical volatility for the stock. Think of solving for one day of theta in an options pricing model.