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