Calculating 1SD move of the underlying

[LM3886]

I'm wondering how people here calculate the one standard deviation move of the underlying, I've not found a formal definition of it and there could be a few choices for vol in sqrt(T) * vol.

Does one use IV or HV for vol? If using IV, does one just use the ATM IV or take into account the IV skew? When there are multiple expiration dates available that cover T (the time period in question), does one use the nearest expiration or some average of multiple expirations?

 

[longandshort]

1. Take timeseries data like price
2. Calculate log change in price
3. Calculate standard deviation on the log change in price

Do this in excel. Log change is "=LN(X/Y)". Standard deviation is "=stdev.s(data)"

 

[stepandfetchit]

I have been using this form for expected move as % of spot: for down move: exp(-ATM_VI*(days/365.25)^.5) ; then exp(ATM_IV*(days/365.25)^.5) for move up.
I think many people use the 30day IV (instead of the ATM IV), which may be an adequate method if you just want to get in the ball park and prefer to overestimate the moves.

 

[panzerman]

Under the assumption of a normal distribution with no skew or kurtosis, 84% of the area under the curve lies to the left of 1SD and 16% to the right. Therefore, there is an 84% probability the underlying will end less than 1SD at the end of the "days" time period. Probability of touching the 1SD value is roughly twice the area to the right or 32%.

The normality assumption says nothing about excursions of price above 1SD and then returning below it.

 

[LM3886]

1. Take timeseries data like price
2. Calculate log change in price
3. Calculate standard deviation on the log change in price

Do this in excel. Log change is "=LN(X/Y)". Standard deviation is "=stdev.s(data)"

I should have been more clear that I'd like to estimate the 1SD underlying move at a future time T from now, not just calculate the historical 1SD move. Although one could use the historical 1SD as an estimate of future 1SD.

 

[jamesbp]

I'm wondering how people here calculate the one standard deviation move of the underlying, I've not found a formal definition of it and there could be a few choices for vol in sqrt(T) * vol.

Does one use IV or HV for vol? If using IV, does one just use the ATM IV or take into account the IV skew? When there are multiple expiration dates available that cover T (the time period in question), does one use the nearest expiration or some average of multiple expirations?

Quick and dirty methods for estimating 1 SD implied move from Vols / ATM straddles

... for #days forward ... Spot x iVol x Sqrt(days/365)
... for #days forward ... ATM Straddle x 1.25 x Sqrt(days/DTE)
... for expiry ... ATM Straddle x 1.25

 

[longandshort]

I should have been more clear that I'd like to estimate the 1SD underlying move at a future time T from now, not just calculate the historical 1SD move. Although one could use the historical 1SD as an estimate of future 1SD.

Implied vol is the 1std that is expected.

 

[Profitaker]

LM3886

HV is backward looking and serves no purpose. IV is the markets expectation of VOL going forward.

So I personally use the IV for the options month that I am trading. I use strike IV to the downside (Puts) which takes into account the Skew and the ATM IV for the upside (Calls) which disregards the Skew.

 

[panzerman]

I should have been more clear that I'd like to estimate the 1SD underlying move at a future time T from now, not just calculate the historical 1SD move. Although one could use the historical 1SD as an estimate of future 1SD.

future_price = current_price*exp(stddev*vol*sqrt(days_in_future/365))

Example: What is the 1SD future price in 20 calendar days of a stock that is currently $45 with a volatility of 25%?

future_price = 45.0*exp(1.0*.25*sqrt(20/365)) = $47.71

or, an 84% probability of the stock finishing below $47.71.

Example:

I want the price with a 90% percent probability that the same stock will finish above a certain value in 20 calendar days.

future_value = 45.0*exp(-1.282*.25*sqrt(20/365)) = $41.74

The naive assumption is no skew or kurtosis. Also, you can use trading days instead of calendar days by using sqrt(trading_days/252). Trading days excludes weekends and holidays.

 

[panzerman]

Want to remove skew and kurtosis from your price data before calculating expected moves?

1) perform a Box-Cox transform on price. The reader can look up this reference.
2) Calculate the future transformed data with the above formula.
3) Back calculate the future expected price using step 2 and the lambda value from the Box-Cox transform.

Y_original = power(Y_transformed*lambda+1,1/lambda)