frolloos


Total Posts: 56 
Joined: Dec 2007 


I know it's all about machine learning these days, but here's a link to something I just wrote on our old friend volatility: https://ssrn.com/abstract=3265046
The very modest contributions of the paper are:
A relationship between vega, vanna, and volga is derived by application of the mixing formula. Given three quoted options the equation automatically gives a robust and accurate approximation for the volatility swap strike, the variance swap strike, and a quantity which we will call the effective correlation. Once the aforementioned quantities have been implied from the three pillar options, the entire volatility skew can be constructed. An additional application of the vegavannavolga relationship is that the volatility skew can be turned into a smile, in other words we give the symmetric smile consistent with the original asymmetric skew. Once the symmetric distribution is derived then in principle options and other derivatives on realized volatility and variance can be priced and hedged 



Strange


Total Posts: 1517 
Joined: Jun 2004 


Pretty interesting, thanks! 
I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 

frolloos


Total Posts: 56 
Joined: Dec 2007 


Thanks. With hindsight I could / should have expanded the section on vol derivs using the symmetrized skew. I'll do that in a revised version down the road. Feel free to contact me if you have questions. 



 