
What are some recommended ways to do this? OTM puts and/or calls on the SPX, or some major SPX components?




nikol


Total Posts: 1403 
Joined: Jun 2005 


In your other thread kloc has given you full explanation. SPX options are proxy of vega vol of SPX Vega on VIX is proxy of vega vol of vol of SPX. 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 


I appreciate kroc's explanation and I dont disagree, but I am working with the full set of options anyhow and developing my own software plugging into interactive brokers to calibrate the model and help with managing positions
when you say "vega vol" you mean just vega right? Or are you referring to the volatility of the timevarying vega?
I mistyped in my other thread, I should have said SPX risk premium based on a joint calibration of VIX and SPX options, as in the quadratic rough Heston process at
https://arxiv.org/abs/2001.01789
This paper entitled Perfect hedging in rough Heston models could also be relevant.
what is "vega vol of vol"?
VVIX is the volatility of VIX too bad there are no options are futures on it..
how can SPX options be a proxy for "VEGA vol" when vega is an attribute of options?
I've read over the CBOE whitepaper and implemented the VIX calculation from the underlying SPX options so I think my confusion lies in semantics/jargon.
There is also this: https://www.sciencedirect.com/science/article/abs/pii/S1059056015001835 but i dont think its what I'm looking for.
The quadratic rough Heston process is appealing because it arises naturally from the microscopic Hawkes process based model which I understand quite well and wrote a paper about and corresponded with the authors about. https://drive.google.com/file/d/1DHYQPvHV9ZXa1fa_gm9fuMfIbk2MIFO3/view?usp=sharing
My main goal is to infer the stochastic process parameters from SPX and VIX options but the secondary goal is to get vega as close to 0 as possible.
another decent paper is at
https://qmro.qmul.ac.uk/xmlui/bitstream/handle/123456789/45763/Gourier%20Inferring%20volatility%20dynamics%20and%20risk%20premia%20from%20the%20S%26P%20500%20and%20VIX%20markets%202018%20Accepted.pdf?sequence=1&isAllowed=y
Thanks for your help




nikol


Total Posts: 1403 
Joined: Jun 2005 


I mean this: vega = dp/dv, where p  price, v  volatility of SPX = VIX dy/dx = y' , derivative of y(x) by x
similarly, vega on VIX = dv/dw, where w  volatility of VIX (vol of vol of SPX)
By saying "options are proxy of X" I say "options depend on information about X".
Heston has vol of vol as a parameter (dzeta, variance of vol). It is responsible for how quickly LVOL surface gets broadened by going from the near term to the far term. This one is calibrated from SPX options.
However, if you can trade VIX options, then it is very different story. http://www.cboe.com/products/vixindexvolatility/vixoptionsandfutures/vixoptions
In this case you can imply vol of vol of SPX (= vol of VIX) directly from VIX options. I saw froloos (in this forum) is researching this stuff, ask him. 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 


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