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Tuesday, June 25th 2019

# Implied Volatility Term Structure's Three Parameters

The implied volatility term structure can be summarized into 1) the 30 day IV 2) the 2 year IV and 3) the implied earnings effect.

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Summary

The implied volatility term structure can be summarized into the 30 day IV, the 2 year IV, and the implied earnings effect. These three parameters are used to summarize most of the term structure. The earnings effect is the percentage by which a stock will move on an earnings announcement. Other parameters that apply to term structure include seasonal term adjustments and short-term IV ATM slope, and other parameters that apply to the monthly strike IV skew, such as slope, derivative, additional call/put wing amounts, and residual yield.

Important information on a ticker is found in the implied volatility (IV) term-structure parameters. The three most important parameters are:

• the 30 day constant maturity implied volatility
• the 2 year constant maturity implied volatility
• the implied earnings effect

Using these three parameters most of the term structure can be summarized.

Let's take an example from today, 6/24/2019, NVDA.

The steps to summarizing the term structure are to:

• Gather the at-the-money (ATM) IVs for each month. ORATS Money API call brings in the 'vol50', the smoothed volatility at the 50 delta in the picture above.
• Take the square root of the days to expiration
• Find the earnings month
• Set up a time skew that draws a curve from the 30 day IV and 2 year IV. ORATS uses a proprietary method but there are models on the web or any curve can be tried. Above the column 'unadjVol' corresponds to this skew calculation.
• Calculate the earnings effect and add to the expirations that occur after the next earnings announcement as in 'EarnEffect' above. Add these effects to the 'unadjVol' to get the 'calVol' or calculated vol.
• Simultaneously solve for the three parameters to the skew that minimizes the difference between the actual volatilities 'vol50' and the calculated volatilities in 'calVol'.

For NVDA today we would say the the 30 day implied volatility ex-earnings is 36.12% and the 2-year IV is 33.96%, and the implied earnings effect is 277%. A way to think about the implied earnings effect is that on the earnings announcement, the stock will move at 277% of its implied volatility.

There are other parameters that apply to term structure like seasonal term adjustments and short-term IV ATM slope (we call Contango), and other parameters that apply to the monthly strike IV skew, such as slope (skew), derivative (kurtosis), additional call/put wing amounts, and residual yield but these are not as important as the big three above and are the subject of other posts.

Moreover, there are more constant maturity calculations that are provided in the ORATS Data API, but the point of this exercise is to use as few parameters as possible to summarize the implied volatilities, with a tip of the hat to Ockham's razor.

References:

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