Moneyness formula for vol surface question


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Bruno: You suggested including sigma in the moneyness formula when rendering volatility surface. I have not done this, but have interest in better understanding it.
Below is a slide you included in an earlier presentation, that I think reflects this point. IF so, can you clarify the origin of the sigma being used? and/or point me to more detail? -- {The Red note is "from where? ATM volatility per DTE?}

Update: Seems that Wikipedia suggests using the ATM IV per DTE, so will try that!


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I took today's SPX pricing at 13:15 Pacific, and plotted the IV surface using Moneyness with and without dividing by ATM_IV. The impact of dividing by ATM_IV (which I have not been doing), magnifies the X-Axis. I remain too ignorant to see value of scaling the X axis by ATM-IV. Below are two plots from today that try to reflect similar views.

Not sure this is of any interest to others, but I wanted to post it before I forget what I did!


Hi Gary, you've done a great job so far. As you have noticed using straightforward moneyness is the way to go to represent similarities across individual vertical skews. The additional factor I introduce doesn't have anything to with price. It just helps compensating or say calibrating the horizontal skew across different DTE. The goal is of course to model projected IV as a function of strike and time to expiration and the simplest the overall shape the easier it will be. Adding a ATM IV in the denominator can be the trick or you could also use a polynomial regression of the VIX Central curve.
Once you have a good looking data set, you can apply a multi-dimensional non-linear regression as explained in this paper from Dumas-Whaley-Fleming.
Any model has its ups and downs and of course choosing this non-parametric route may not be the one academics would prefer but as I said in the last session, I do believe that using bivariate stochastic model to account for vol behaviour is either an overkill or too fuzzy to be of practical use. The mean reversion aspect is undeniable however not easy to work with. CEV is one attempt to add mean reversion into the equation but I'd rather pass and stick to a non parametric model that one can recalibrate frequently.
You may find that non linear regression a little too complicated but it isn't really and you can find good open source libraries like MathNet to do the bulk of it for you. I'll help you through it. At the end of the day only a model (with its flaws) can turn intuition from interesting market data into something of practical use.
We can discuss later on how to deal with concavity (S.Speer uses a local approach in one of his papers) and little tweaks to the Raphson-Newton algorithm to improve the whole thing.

This may be the topic for the next session actually then once we have all our ducks in a row, we'll be in a better position to see how it can provide us with trading opportunities like what you intuitively pointed out on evolving concavity across DTE.



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Bruno: While many of the concepts you and Steve S. describe are beyond my immediate reach, I do pick up a few nuggets along the way that move me to a better understanding of the behavior of IV. I now embrace the "standardized moneyness" as a better view of moneyness for IV surface observations. Thanks for nudging me to take a closer look at this!

The Wikipedia description is good:
... Dispersion is proportional to volatility, so standardizing by volatility yields:[9]

This is known as the standardized moneyness (forward), and measures moneyness in standard deviation units.