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I'm currently working on my master thesis, where I have data on option trading volume and flow (number of shares bought minus sold; i.e., net position), divided among three kinds of market participants (Agent, Market Maker and Prop). The data is for European equities.

An Implied volatility (IV) surface has time to maturity on the X-axis, moneyness (Underlying Price/Strike) on the Y-axis and IV on the Z-axis. Similar to it, I have constructed a Greek surface, where the Z-axis is a greek, for example, delta.

As part of my analysis, I wanted to study the evolution of Greek surfaces over time and if it can tell us something about the future activity of a given participant. For example, look at the following image. It is the Delta position by market participant over time. As you would expect, market makers tend to stay neutral to the market.

Delta position by market participant

However, this is too simplistic to gain an edge in the market. As mentioned, what I am interested in analysing the dynamics of surfaces.

enter image description here enter image description here enter image description here

To do so, I would need to parameterise the surfaces in a way that I can study their dynamics over time. By parameterisation, I mean reducing the number of parameters to about 4-5.

Hence, I am looking for ideas on how to do this parametrisation. Any ideas would be appreciated!

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    $\begingroup$ If you're calculating these greeks using the black scholes formulae, then all you need is the vol surface. If you can get the vol surface parameterised in 4-5 parameters, then you have everything else you need. A functional form with just 4-5 parameters that gives you an accurate representation of the full vol surface is not trivial, but it sounds like it's not the subject of your thesis. I would suggest using someone elses' functional form for this - perhaps the SVI models of jim gatheral are a decent place to start. $\endgroup$
    – will
    Jun 29 '21 at 20:10
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This will not help you with the actual question but I think the theta surface should look differently. I have a simplified solution where it is all with sliders to play around for teaching purposes (vol is constant throughout and simply an input from the slider into BSM). The sliders at the top are strike, interest rate, dividend and vol; bottom is just "camera" settings for moving the 3d surface and its alpha.

I think theta should be biggest in absolute values around ATM. Usually it is customary to use less time to maturity, so you have negative theta.
enter image description here

This is a simpler chart that matches the 3D logic above. enter image description here

There are other websites that also follow my logic like the Wolfram Demonstrations Project enter image description here

Or a related question here.

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