1 Sigma

[wxytrader]

Is this basically the equivalent of a 3 SD move?
Black Scholes for SPY expiring Dec29 with 50% IV is:
459.63/489.53

Based on the last 30 days of closing prices the sigma comes to:
443.37/483.95

 

[destriero]

Sigma = SD.

 

[wxytrader]

"Sigma is a statistical measurement of variability, showing how much variation exists from a statistical average. Sigma measures how far an observed data deviates from the mean or average; investors use standard deviation to gauge expected volatility, which is known as historical volatility."

Ok so it can be a substitute for BS without needing IV.

 

[Quanto]

Ok so it can be a substitute for BS without needing IV.

IV = sigma * 100
And yes, 1 sigma = 1 SD
Black-Scholes uses the IV (actually the sigma), and is something different...

Is this basically the equivalent of a 3 SD move?
Black Scholes for SPY expiring Dec29 with 50% IV is:
459.63/489.53

Based on the last 30 days of closing prices the sigma comes to:
443.37/483.95

Hmm. that's not sigma, nor IV.
Why do you have pairs of values? Do they represent the starting and ending values maybe?
The SPY Call ATM IV for ExpDate 2023-12-29 as of now (2023-12-22T14:00:00 EST) is about 12, and about 8 for the Puts, according to YahooFinance (if their data is correct).

 

[destriero]

"Sigma is a statistical measurement of variability, showing how much variation exists from a statistical average. Sigma measures how far an observed data deviates from the mean or average; investors use standard deviation to gauge expected volatility, which is known as historical volatility."

Ok so it can be a substitute for BS without needing IV.

No for many reasons, but HV would have you short vol (or long calendars) indiscriminately into events; CPI, SN-earnings, etc.

 

[wxytrader]

IV = sigma * 100
And yes, 1 sigma = 1 SD
Black-Scholes uses the IV (actually the sigma), and is something different...


Hmm. that's not sigma, nor IV.
Why do you have pairs of values? Do they represent the starting and ending values maybe?
The SPY Call ATM IV for ExpDate 2023-12-29 as of now (2023-12-22T14:00:00 EST) is about 12, and about 8 for the Puts, according to YahooFinance (if their data is correct).

(459.63/489.53) are the 1 standard deviations for price by 12/29

 

[wxytrader]

No for many reasons, but HV would have you short vol (or long calendars) indiscriminately into events; CPI, SN-earnings, etc.

I could always pull data from the entire year to smooth it out and skip high volatility events or pull data from previous high volatility events...this is basically just to have my spreadsheet calc on average the stock moves x amount per day without having to look up IV or ATR or api. ATR only uses price data no IV so maybe I'll do both and compare which turns out more accurate.

 

[destriero]

I could always pull data from the entire year to smooth it out and skip high volatility events or pull data from previous high volatility events...this is basically just to have my spreadsheet calc on average the stock moves x amount per day without having to look up IV or ATR or api. ATR only uses price data no IV so maybe I'll do both and compare which turns out more accurate.

No. You have to arrive at a model for the switch (D1/D2 (duration)). Smoothing would be death. You cannot simply ignore IV.

 

[Quanto]

(459.63/489.53) are the 1 standard deviations for price by 12/29

Ok, got it now: price at -1SD and at +1SD, right.

BUT I think your numbers for -1SD and +1SD cannot be correct if you take IV=50 and DTE=8, as you said in your OP. And I wonder why you mention Black-Scholes, b/c it's irrelevant in this calculation. That's confusing...

 

[Quanto]

For S=473, IV=50, DTE=8 one gets these results for -1SD and +1SD:

S=473.0000 IV=50.00 DTE=8.00(t=0.021918) rPct=0.00 qPct=0.00 z=-1.00 --> Sx=439.2514 dSx=-33.7485(-7.13%)

S=473.0000 IV=50.00 DTE=8.00(t=0.021918) rPct=0.00 qPct=0.00 z=+1.00 --> Sx=509.3414 dSx=36.3415(7.68%)