Stochastic Volatility vs Vanna-Volga

Question

I'm working on the calibration of the Heston Stochastic Volatility Model for some FX option data for my bachelor thesis and I was asked "Why should people use Heston instead of other simple approach like Vanna-Volga (VV)?".

According to my research, the greatest point in favor of stochastic volatility models is that volatility seems to behave stochastic, also it may be useful in iliquid markets where only few data is availabe. The pros of the Heston model is that it contains a semi-closed formula for vanilla options, which makes calibration easier, and it doesn't assume log-normality, so it captures better the asymmetry and kurtosis. The cons are that for short maturities it may be impossible to calibrate the model.

On the other hand, VV is an interpolation method which is arbitrage-free and needs only 3 volatility quotes (commonly 25$\Delta$ BFY, 25$\Delta$ RR, ATM). The first point that comes to my mind is that maybe when we also have the 10$\Delta$ BFY and 10$\Delta$ RR, VV may not be able to fit the 5 points.

In summary:

1. What are the disadvantages of the Vanna-Volga method?
2. What are the advantages of Heston model (or stochastic volatility models in general) over Vanna-Volga?

Any paper, book or other source is welcome. I also share some of my sources.

• https://www.coursehero.com/file/42365761/calibrating-hestonpdf/
• https://mathfinance.com/wp-content/uploads/2017/06/FXOptionsVannaVolga.pdf
• https://papers.ssrn.com/sol3/papers.cfm?abstract_id=873788
• Antonio Castagna - FX Options and Smile Risk-Wiley (2010)
• Jim Gatheral, Nassim Nicholas Taleb - The Volatility Surface - A Practitioner's Guide (Wiley Finance)-Wiley (2006)

Answer 1

Vanna-Vega-Volga is a cute way of interpolating the fx implied volatility surface. The problem is that the vols coming from that interpolation do not match the interbank quoted volatilities, you can't match the 10 delta wings without some weird contortions and using that methodology for first generation exotics results in the incorrect market price. To be fair the same is true for Heston but it has the added benefit of being the base model for a lot of the more sophisticated models you do need to match first generation fx exotics.