I am currently researching a pre-print article by Julien Guyon & Jordan Lekeufack (2022): Volatility Is (Mostly) Path-Dependent.
Their model is quite impressive in both its simplicity, as well as its efficacy. However, I have one fundamental question in doing research about the joint calibration of the SPX and VIX.
The question is simply: why?
The continued answer to this question, which I've found in other articles, is a hand wavy response that there might be arbitrage otherwise. However, I have never seen such an example put forward.
The only sensible heuristic reasoning I've come up with is that:
- The SPX and VIX are intrinsically linked by definition. Regarding pricing, we would not want to price e.g. SPX put options and VIX call options too differently.
Lastly, another source of confusion is the fact that the model being put forward of the underlying uses VIX as its volatility parameter. Shouldn't the model of an underlying use realised volatility?