If you need fully automated vol surface calibration from option prices which is fast, reliable, bias-free and arb-free, works with cash dividends and has any other industry standard bells and whistles (vol time, microprices, temporal filtering etc) you should check out Vola Dynamics . PS. Disclaimer...

For formal methods you can search for utility indifference pricing.

The general principle is that you should price the risk factors you can hedge at the price of hedging plus the cost of doing business and the risks you cannot hedge at the unbiased estimate under P measure plus the cost of capital associated with holding the corresponding risk. If you are a market m...

There are several ways to address this problem, some work only in HFT context while other are applicable at the level of snapshot data as well.
PM me if you want to discuss.

If you need an industrial-strength solution you can check out Vola Dynamics (disclaimer - I am affiliated).

Here is an example of a fully automated fit right before Brexit:

https://www.voladynamics.com/marketIndexEU_AEX.html

The fits are parametric, arb-free, very robust, and fairly fast.

What's the definition of "equivalent volatility"?
What are you trying to achieve?

It can be below 0 or above 1.

On the subject of delta calculation take a look at this article:
https://www.linkedin.com/pulse/spot-vol ... y-klassen/

Do a simple exercise. Calculate how much you will lose on 100K short vega sold at 10 which realizes 100.

Var swaps are easy to price and replicate. Vol swaps don't have extreme payoffs in the tails but are model dependent and do not have static hedges.

EAZL, conceptually the problem does not sound hard. However, the devil is in the details. Production quality implementation involves many steps. The set of issues is somewhat different for liquid and illiquid names. Vola Dynamics offers a very comprehensive and robust solution to the problem of cali...

A good starting point would be VIX white paper and a primer on var swaps.

Both sticky strike and sticky delta assumptions lead to arbitrage (see this https://math.unice.fr/~diener/nicemathfi03/Bruno_Dupire_vol_presentation_1302c.ppt ). Both sticky strike and sticky delta are not consistent with how implied volatilities move in liquid competitive markets (btw, which underl...

We don't have any paper in the public domain at the moment. There are several components which are important: 1) Robust fitting of parametric bias-free and arbitrage volatility surfaces. With a vol surface one can price a log contract. 2) Estimation of the distribution for the variance.  3) Volatili...

What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging?  Check out this post on consistent valuation and risk management of vol derivatives and vanilla options: https://www.linkedin.com/pulse/vo...

I am interested to take price (or rather, returns) data and divide it to n periods, according to distribution moments, in a way that will create the best separation. How do you approach that?

what is the metric by which different classifications will be compared? what are you trying to accomplish?

take a look at the paper on dividend modeling from here
https://www.voladynamics.com/research.html