The visual depiction of the ATF call:
For the ATF strike the call and put have the same value!
<aside> ℹ️ About
This post explores the relationship between an option straddle and volatility.
You will learn:
The Difference Between SD and MAD
<aside> 🔑 Key Takeaways
If the underlying distribution is Gaussian:
You could expect the ratio to differ for non-Gaussian distributions. When examining data, computing both statistics can give you a clue about its nature.
In the text example above, the MAD/SD ratio of only 27% is a clue:
Even though the MAD is more useful than SD for telling us what outcomes are typical, the ratio indicates that there are some highly skewed outliers.
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<aside> 🔑 Key Takeaways
The visual depiction of the ATF call:
For the ATF strike the call and put have the same value!
which yields…
where:
S = forward price
σ = annualized volatility
t = fraction of a year until expiry
<aside> ⏪ In case you want to walk through it again:
Visual Derivation of Straddle Approximation
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Look at the key takeaways thus far. What do you see?
The mean absolute deviation is .80 of the standard deviation and the straddle is .80 of the volatility.
The straddle is the MAD!
The volatility, which is computed just like a standard deviation, gives large moves extra weight. But the straddle is a better reflection of what move size we typically see.
It will cost you .80 of the standard deviation to buy a fairly priced straddle. Let’s plug that into a normal curve’s cumulative distribution function:
