ORATS describes the implied volatility surface as a 3-dimensional surface where the independent variables are time to expiration, and option delta and the dependent variable is implied volatility. To illustrate an implied volatility surface, we have developed a 2-dimensional graph that displays all three axes in the figure below. Summary information about this surface gives the trader a macro view of the implied volatilities for each option chain. ORATS takes a snapshot of all options on all symbols approximately 14 minutes before the close of trading. Options markets from this time are often of higher quality than at the close.

ORATS measures the surface using the following summary characteristics: at-the-money volatility, strike slope, and derivative (curvature).

 

[​IMG]

Delta is best to use on the x-axis as was said earlier it normalizes the skew so you can compare different expirations and different stocks.

Strike Slope is a measure of the amount that implied volatility changes for every increase of 10 call delta points within the intra-month skew. It measures how lopsided the 'smile' or 'smirk' is. The derivative is a measure of the rate at which the strike slope changes for every increase of 10 call delta points within the intra-month skew. It measures the curvature of the intra-month skew or 'smile.' We chose just two parameters to describe the skew to get a reasonable fit for the fewest assumptions.


We start with lining up the calls and puts IVs using residual yields. We use the 85 to 15 call deltas in the study. We have more weightings to the call an puts for closeness to the 50 delta and we weight the call vs put the more OTM we go, meaning the 20 delta call IV will get more weighting than the same strike 80 delta put: The IVs will be slightly different even after our residual yield process. Then on to estimating the slope with a best fit, and we are left with errors from the slope line to the actual mid market IVs. We apply the derivative to minimize those errors.

We create a slope & derivative not to create our smooth market values but to create parameters for comparison to other months in the same security and to other securities.
Our smooth market values process starts with a process akin to a cubic spline and then this spline is adjusted to strike IVs in a localized methodology. This process creates a very accurate theoretical values to the market bid-ask, being in between ~99% of the time.
After the SMV process we then calculate a slope & derivative. This is an intricate process developed over many years and with much trial and error.

In our service all this can be graphed historically on our web tool or downloaded in our API.

For example, IYR's slope looks cheap and XME's slope looks expensive from a variety of measurements:

[​IMG]

 

1. We have a forecast of slope and that forecast is above IYRs current slope.

2. IYR has a relatively low slope percentile vs say XME whose slope percentile is higher, see below.

3. ORATS also has a measurement of the component averages for all readings including slope, and slope percentile. The ratio of IYR's components slope to IYR's slope makes the ETF look cheap and opposite for XME.

4. We also compare the ETFs to the SPY and track the relationship. For stocks, we track the relationship of the best ETF.

 

[​IMG]

 

If you look in our documentation you can see the names and descriptions. We also have blogs about slope.

https://docs.orats.io/data-api-guide/definitions.html#core-general

https://blog.orats.com/hs-search-results?term=slope&type=BLOG_POST&id=6125614442

slopepctile one-year percentile for the slope
slopeavg1m slope average for trailing month
slopeavg1y slope average for trailing year
slopeStdv1y standard deviation of the Slope
etfSlopeRatio slope divided by ETF slope current
etfSlopeRatioAvg1m slope divided by ETF slope month average
etfSlopeRatioAvg1y slope divided by ETF slope year average
etfSlopeRatioAvgStdv1y slope divided by ETF slope year standard deviation
Here are a sampling of more fields:
annIdiv annual implied dividend given options prices put call parity
borrow30 implied hard-to-borrow interest rate at 30 days to expiration given options prices put call parity
confidence total weighted confidence from the monthly implied volatilities derived from each month’s number of options and bid ask width of the options markets
exErnIv10d implied 10 calendar day interpolated implied volatility with earnings effect out
iv10d 10 calendar day interpolated implied volatility
impliedMove percentage stock move in the implied earnings effect to make the best-fit term structure of the month implied volatilities
mwAdj30 ATM weighted market width in implied volatility terms interpolated to 30 calendar days to expiration
rDrv30 derivative or curvature of the monthly strikes at 30 day interpolated. The derivative is the change in the slope for every 10 delta increase in the call delta
dlt25Iv1y 365 calendar day interpolated implied volatility at the 25 delta
dlt95Iv6m 180 calendar day interpolated implied volatility at the 95 delta
fwd60_30 The forward volatility extracted from the 60 day and 30 day implied volatility
ffwd180_90 The flat forward volatility extracted from the 180 day and 90 day implied volatility

 

Notes: We use a binomial tree approach as described in Haug "The Complete Guide to Option Pricing Formulas". We use percentage of a day starting at 95% at the open and 5% at the close. Pricing models generally don't work with 0 DTE. We calculate a confidence level for each expiration, so that would be the error term for the IV. We calculate historical goodness of fit for our forecasts, and that is the error term for your comparison.

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