A good options trader knows that implied volatility is driven by supply and demand for options in the market. However, there is also a general risk premium for selling options which means that implied volatility should usually trade at a premium to the realized volatility of the asset. The risk premium can go up and down, but generally, it reverts to a mean level.

One of the opportunities available to traders is to look to capture mispricings in the cross-asset volatility markets due to structural flows in the market that market makers/dealers (money center banks) are unable to keep in inventory. This could lead to the spread (difference A - B) between implied volatilities in two asset classes reaching stretched levels. Normally, this level of stretchiness can be measured by something like a z-score. What is a z-score? Good question. This is a measurement of how far the current spread is from its historical range. It is defined as:

**(x - mu)/sigma over a historical range of time i.e. the last 1 year.**

mu is the mean of the sample over the historical range and sigma is the standard deviation of the sample over the historical range.

That is, if the z-score is 1 it means the spread is currently at 1 standard deviation of its long-term average. If the z-score is -1 that means the spread is similarly far from its historical average, but the spread is in the opposite direction (i.e. A is undervalued vs B).

**What kind of a z-score would it require for me to put a mean reverting cross-asset volatility trade on? **

If you recall some basics of your statistics classes, 68% of observations will fall within 1 standard deviation of the mean while 95% of observations will fall within 2 standard deviations of the mean, assuming a normal distribution. This is referred to as the 68-95-99.7 rule.

In the next tutorial, we'll go over what levels of z-scores to start scaling into cross asset class relative value volatility trades, how to calculate these z-scores, and sample trades. Until next time**!**

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